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Q:

Factor the polynomial function $$f ( x )$$ . Then solve the equation $$f ( x ) = 0$$ .

$$f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 9 x - 18$$

The factored polynomial function is $$f ( x ) = \square$$ . (Factor completely.)

The solutions of the equation $$f ( x ) = 0$$ are $$\square$$ .

(Use a comma to separate answers as needed.)

Q:

A town currently has $$4000$$ residents. The expected future population can be approximated by the function $$p ( x ) = 4000 ( 1.117 ) ^ { 0.1 x }$$ where $$x$$ is the number of years in the future. Determine the expected population of the town in $$10$$ years, and in $$50$$ years.

A) $$5,225$$ and $$7,358$$

B) $$40,445.04$$ and $$202,225.22$$

C) $$4,468$$ and $$1.78 \times 1018$$

D) $$4,468$$ and $$6,955$$

Q:

A ball is shot from a cannon into the air with an upward velocity of $$40 ft / sec$$ . The equation that gives the height (h) of the ball at any time ( $$t )$$ is: $$h ( t ) = - 16 t ^ 2 + 40 ft + 1.5$$ . Find the maximum height attained by the ball.

Q:

Find an equation of the line having the given slope and containing the given point. Then graph the line passing through the given point and having the given slope on the provided graph worksheet or graph paper.

$$m = 0 , ( 0 , - 6 )$$

The equation of the line is $$y = \square$$ Use the provided graph worksheet or graph paper to graph the line and upload a picture of your graph in the following question. Use the given point and slope when drawing the line.

Q:

For the graph shown below do the following.

a. Find the zeros and state the multiplicity of each zero.

b. Write an equation, expressed as the product of factors, of a polynomial function for the graph. Use a leading coefficient of $$1$$ or - $$1$$ and make the degree of $$f$$ as small as possible.

c. Use both the equation in part (b) and the graph to find the $$y$$ -intercept

a. List the zeros whose multiplicity is even. Select the correct choice below and fill in any answer boxes within your choice.

A. $$\square$$(Use a comma to separate answers as needed.)

B. There are no such zeros.

List the zeros whose multiplicity is odd. Select the correct choice below and fill in any answer boxes within your choice.

A. $$\square$$(Use a comma to separate answers as needed.)

B. There are no such zeros.

b. Write an equation, expressed as the product of factors, of a polynomial function for the graph. Use a leading coefficient of $$1$$ or $$- 1$$ and make the degree of $$f$$ as small as possible.

$$f ( x ) = \square$$

c. The y-intercept is $$\square$$

Q:

Find (a) the slope (if it is defined) of a line containing the two given points, (b) the equation of the line containing the two points in slope-intercept form, and (c) the ordered pair identifying the line's y-intercept, assuming that it exists. If appropriate, state whether the line is vertical or horizontal.

$$( \frac { 3 } { 10 } , - 5 )$$ and $$( - \frac { 1 } { 5 } , - \frac { 1 } { 5 } )$$

a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The slope is

B. The slope is undefined.

Q:

Suppose that the point $$( x , y )$$ is in the indicated quadrant. Decide whether the given ratio is positive or negative. Recall that $$r = \sqrt { x ^ { 2 } + y ^ { 2 } }$$ .

$$I I , \frac { r } { x }$$

In Quadrant II, is $$\frac { r } { x }$$ positive or negative?

$$\circ$$Negative

$$\circ$$Positive

Q:

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solve

$$e ^ { 1 - 7 x } = 2173$$

The solution set expressed in terms of logarithms is $$\{ \frac { 1 - \ln 2173 } { 7 } \}$$ . (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression. Use In for natural logarithm and log for common logarithm.)

Now use a calculator to obtain a decimal approximation for the solution. The solution set is $$\square$$

(Use a comma to separate answers as needed. Round to two decimal places as needed.)

Q:

A certain electronics manufacturer found that the average cost $$C$$ to produce $$x$$ DVD/Blu-ray players can found using the equation $$C = 0.04 x ^ { 2 } - 5 x + 700$$ . What is the minimum average cost per machine and how many DVD/Blu-ray players should be built in order to achieve that minimum?

The minimum average cost is $$\square$$

The number of DVD/Blu-ray players that should be build to achieve the minimum is $$\square$$

*Answer both to the nearest whole number.

Q:

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable. See Examples 1-5. 31. $$y = 2 \sin ( x + \pi )$$

32. $$y = 3 \sin ( x + \frac { \pi } { 2 } )$$

33. $$y = - \frac { 1 } { 4 } \cos ( \frac { 1 } { 2 } x + \frac { \pi } { 2 } )$$

34. $$y = - \frac { 1 } { 2 } \sin ( \frac { 1 } { 2 } x + \pi )$$

35. $$y = 3 \cos [ \frac { \pi } { 2 } ( x - \frac { 1 } { 2 } ) ]$$

Q:

The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $$\ 4 ,$$ sales will reach $$7000$$ Fun Noodles per day during the summer. Raising the price to $$\ 5$$ will cause the sales to fall to $$6000$$ Fun Noodles per day

a. Assume that the relationship between sales price, $$x$$ , and number of Fun Noodles sold, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (sales price, number sold)

The equation is $$\square$$ . (Type your answer in slope-intercept form.)

Q:

Solve for $$n$$ in the equation below. It may be helpful to convert the equation into exponential form.

$$\log _ { 6 } 216 = n$$

$$n =$$ __

Q:

Solve for $$n$$ in the equation below. It may be helpful to convert the equation into exponential form.

$$\log _ { 6 } 216 = n$$

$$n =$$ __

Q:

Find the domain of $$y = \log ( 3 + 4 x )$$

The domain is:

$$x \geq A$$

$$x \leq A$$

$$x < A$$

$$x > A$$

Q:

Write $$3 \log x - 4 \log ( x ^ { 2 } + 1 ) + 2 \log ( x - 1 )$$ as a single logarithm. Assume all arguments represent positive numbers.

$$\log ( \square )$$

Q:

In one baseball season, Peter hit twice the difference of the number of home runs Alice hit and $$3$$ . Altogether, they hit $$9$$ home runs. How many home runs did each player hit that season? Let $$h$$ represent Alice's home runs.

Q:

Find $$( f - g ) ( x )$$ if $$f ( x ) = \sqrt { 4 x }$$ and $$g ( x ) = \sqrt { 16 x }$$

$$( f - g ) ( x ) = - 2 x$$

$$( f - g ) ( x ) = - 2 \sqrt { x }$$

$$( f - g ) ( x ) = 2 \sqrt { x }$$

$$( f - g ) ( x ) = 6 \sqrt { x }$$

Q:

Find $$( f + g ) ( x )$$ if $$f ( x ) = - 3 x ^ { 2 } + 2 x - 3$$ and $$g ( x ) = 2 x ^ { 2 } - 3 x + 4$$ $$( f + g ) ( x ) = - x ^ { 2 } - x + 1$$

$$( f + g ) ( x ) = - 5 x ^ { 2 } + 5 x - 7$$

$$( f + g ) ( x ) = x ^ { 2 } + x - 1$$

$$( f + g ) ( x ) = 5 x ^ { 2 } - 5 x + 7$$

Q:

Suppose that $$f ( x ) = - 7 x ^ { 2 } - 2 x$$

(A) Find the slope of the line tangent to $$f ( x )$$ at $$x = 3$$

(B) Find the instantaneous rate of change of $$f ( x )$$ at $$x = 3$$

(C) Find the equation of the line tangent to $$f ( x )$$ at $$x = 3 \cdot y = 1$$

Q:

Find $$( f \cdot g ) ( x )$$ if $$f ( x ) = x ^ { 2 } + 2 x + 4$$ and $$g ( x ) = x - 2$$

$$( f \cdot g ) ( x ) = x ^ { 3 } + 4 x ^ { 2 } + 8 x - 8$$

$$( f \cdot g ) ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 8 x + 8$$

$$( f \cdot g ) ( x ) = x ^ { 3 } + 8$$

$$( f \cdot g ) ( x ) = x ^ { 3 } - 8$$

Q:

Find $$( \frac { f } { g } ) ( x )$$ if $$f ( x ) = x ^ { 2 } + x + 1$$ and $$g ( x ) = - x ^ { 2 } - x - 1$$

$$( \frac { f } { g } ) ( x ) = - 1$$

$$( \frac { f } { g } ) ( x ) = - x$$

$$( \frac { f } { g } ) ( x ) = x$$

$$( \frac { f } { g } ) ( x ) = 1$$

Q:

(1 point) Given the function

$$f ( x ) = 3 x ^ { 2 } + x + 1$$

find the following.

(a) the average rate of change of $$f$$ on $$[ - 1,2 ] :$$ _____

(b) the average rate of change of $$f$$ on $$[ x , x + h ] :$$ _____

Q:

What is $$( g \circ f ) ( - 2 )$$ if $$f ( x ) = 3 x - 1$$ and $$g ( x ) = 4 x ^ { 2 } + 9 ?$$

$$( g \circ f ) ( - 2 ) = 145$$

$$( g \circ f ) ( - 2 ) = 74$$

$$( g \circ f ) ( - 2 ) = 205$$

$$( g \circ f ) ( - 2 ) = 109$$

Q:

What is $$( f \circ g ) ( x )$$ if $$f ( x ) = 2 x + 3$$ and $$g ( x ) = \frac { x } { 4 } ?$$

$$( f \circ g ) ( x ) = \frac { 3 } { 4 } x + \frac { 1 } { 2 }$$

$$( f \circ g ) ( x ) = \frac { 1 } { 2 } x + \frac { 3 } { 4 }$$

$$( f \circ g ) ( x ) = \frac { 1 } { 2 } x + 3$$

$$( f \circ g ) ( x ) = \frac { 1 } { 2 } x + \frac { 3 } { 2 }$$

Q:

Solve.

$$x = - 7$$

$$- x - y = - 1$$

Q:

Solve.

$$4 x + y = - 3$$

$$3 x + 3 y = 18$$

Q:

A line has a slope of $$5$$ and passes through the point $$( 2,0 )$$ . What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

$$y = \square x - \square$$

Q:

A line that includes the point $$( 0 , - 4 )$$ has a slope of $$- 4$$ . What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

$$y = \square x - \square$$

Q:

A line has a slope of $$5$$ and passes through the point $$( 2,0 )$$ . What is its equation in slope-intercept form? Write your answer using integers, proper fractions, and improper fractions in simplest form.

$$y = \square x - \square$$

Q:

There is a line that includes the point $$( 0 , - 1 )$$ and has a slope of $$- 7 .$$ What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

$$y = \square x - \square$$

Q:

Using the given graph of the function $$f$$ , find the following.

(a) the intercepts, if any

(b) its domain and range

(c) the intervals on which it is increasing, decreasing, or constant

(d) whether it is even, odd, or neither

(a) What are the intercepts?

____

Q:

Use the graph of the function $$f$$ given below to answer the questions.

List the values of $$x$$ at which $$f$$ has a local minimum. Select the correct choice below and fill in any answer boxes within your choice.

A. $$x = \square$$ (Type an integer. Use a comma to separate answers as needed.)

B. There are no local minima.

Q:

For a certain company, the cost for producing $$x$$ items is $$50 x + 300$$ and the revenue for selling $$x$$ items is $$90 x - 0.5 x ^ { 2 }$$ .

The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!

Part a: Set up an expression for the profit from producing and selling $$x$$ items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)

Part b: Find two values of $$x$$ that will create a profit of $$\ 50$$ .

$$x = 1$$ ; $$x - 1$$ ). The order of the list does not matter. To enter $$\sqrt { a }$$ , type sqrt(a).

$$x= \square$$

Part c: Is it possible for the company to make a profit of $$\ 2,500 ?$$

Q:

For the graph of a function $$y = f ( x )$$ shown to the right, find the absolute maximum and the absolute minimum, if it exists.

A. The absolute maximum of $$y = f ( x )$$ is __

(Type an integer or a simplified fraction.)

B. There is no absolute maximum for $$y = f ( x )$$ .

Q:

Which of the following expressions are equivalent? (Select all that are correct).

$$\square \log _ { 10 } 3 = x$$ and $$10 ^ { x } = 3$$

$$\square \log _ { 10 } 10 = x$$ and $$10 ^ { 10 } = x$$

$$\square \log _ { 7 } 10 = x$$ and $$7 ^ { x } = 10$$

$$\square \log _ { 55 } 1 = x$$ and $$1 ^ { 55 } = x$$

Q:

What properties must a probability density function (pdf) satisfy? (2 sentences minimum)

Q:

Suppose that the functions $$u$$ and $$w$$ are defined as follows.

$$u ( x ) = 2 x$$

$$w ( x ) = x ^ { 2 } + 1$$

Find the following.

$$( w \circ u ) ( 2 ) =$$

$$( u \circ w ) ( 2 ) =$$

Q:

Graph the polynomial function $$f ( x ) = \frac { 1 } { 2 } ( x - 2 ) ^ { 2 } + 4$$ . Then answer parts a and b

Use the graphing tool to graph the equation.

a) Determine the largest open interval of the domain for which the function is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The function is increasing on $$\square$$(Type your answer in interval notation.)

B. The function is not increasing on any interval of the domain.

b) Determine the largest open interval of the domain for which the function is decreasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The function is decreasing on $$\square$$ (Type your answer in interval notation.)

B. The function is not decreasing on any interval of the domain.

Q:

Graph the rational function.

$$f ( x ) = \frac { x + 5 } { x + 1 }$$

Q:

Billy rides his bicycle on a straight race track. When he starts sprinting he increases $$2 m / s$$ for every second, $$s$$ , he continues to drive over $$9$$ seconds in the race. At  $$9$$ seconds he is traveling $$10 m / s$$. He Writes the following functions to represent his speed after s seconds but he must combine them somehow:

$$a ( x ) = s - 9$$

$$s ( x ) = 2 s + 10$$

Write a composite function to represent his speed $$s$$ seconds in the race.

Find out how fast he is going after $$14$$ seconds.

Q:

If you apply the changes below to the absolute value parent function, $$f ( x ) = | x | ,$$

what is the equation of the new function?

Shift $$5$$ units right.

Shift $$7$$ units down.

A. $$g ( x ) = | x + 5 | - 7$$

B. $$g ( x ) = | x - 5 | - 7$$

C. $$g ( x ) = | x - 7 | - 5$$

D. $$g ( x ) = | x - 7 | + 5$$

Q:

$$f ( x ) = 3 x + 6 .$$ Find the inverse of $$f ( x )$$

A. $$f ^ { - 1 } ( x ) = 6 - 3 x$$

B. $$f ^ { - 1 } ( x ) = \frac { x - 3 } { 6 }$$

C. $$f ^ { - 1 \cdot } ( x ) = \frac { x - 6 } { 3 }$$

D. $$f ^ { - 1 } ( x ) = 3 x - 6$$

Q:

Suppose $$f ( x ) = x ^ { 2 }$$ and $$g ( x ) = ( 4 x ) ^ { 2 }$$ . Which statement best compares the graph of $$g ( x )$$ with the graph of $$f ( x )$$ ?

A. The graph of $$g ( x )$$ is vertically stretched by a factor of $$4$$ .

B.The graph of $$g ( x )$$ is horizontally compressed by a factor of $$4$$ .

C. The graph of $$g ( x )$$ is horizontally stretched by a factor of $$4$$ .

D. The graph of $$g ( x )$$ is shifted $$4$$ units to the right.

Q:

If $$f$$ is a linear function, with $$f ( 7 ) = 4$$ and $$f ( - 6 ) = - 2$$ .

Determine the slope exactly. The slope is $$m = \square$$

Use your calculate slope and point $$( 7,4 )$$ to setup the equation in point-slope form,

$$y - y _ { 1 } = m ( x - x _ { 1 } )$$

$$\square$$

Now solve for $$y$$ and write the equation of the line in slope-intercept form.

$$y= \square$$

Q:

Timmy gets paid $$\ 20$$ per hour for every hour he works up to $$40$$ hours per week. Over $$40$$ hours per week he gets paid $$\ 40$$ an hour as overtime pay. He writes down two functions with $$x$$ being the hours he works: $$f ( x ) = x - 40$$ , how can you represent his overtime pay as a composite function using the two functions he wrote down.

Q:

Timmy launches a satellite into space. To achieve successful orbit the satellite must reach an altitude

$$60$$ miles above the planet. If the launch of the rocket follows a parabolic path what parabolic feature should he most be interested in?

a) the vertex

b) the axis of symmetry

c) the $$x$$ -intercepts

d) the $$y$$ -intercepts

Why did you answer the way you did?

Q:

The domain of a function $$f ( x )$$ is $$x \geq 0$$ , and the range is $$y \leq - 1$$ . What are the domain and range of its inverse function, $$f ^ { - 1 } ( x )$$ ? A. Domain: $$x \leq 0$$

Range: $$y \geq - 1$$

B. Domain: $$x \geq 0$$

Range: $$y \leq - 1$$

C. Domain: $$x \geq - 1$$

Range: $$y \leq 0$$

D. Domain: $$x \leq - 1$$

Range: $$y \geq 0$$

Q:

Jimmy is in control of anti-alien weapons. A huge alien spacecraft starts attacking earth at an altitude $$80$$ miles above the planet. If the path of his defensive missiles follows a parabolic trajectory and he plans to hit the ship at the top of his weapons parabolic path what parabolic feature should he most be interested in?

a) the $$x$$ -coordinate of the vertex

b) the $$y$$ -coordinate of the vertex

c) the $$x$$ -intercepts

d) the $$y$$ -intercept Why did you answer the way you did ?

Q:

Sally decides to become an awesomenaut. An awesomenaut is just like an astronaut except more awesome. She decides to become an awesomenaut by traveling to planet $$qX$$ . On planet $$qX$$ the gravity is very odd, the gravity is $$1$$ graviton all the way up to $$9.6$$ miles above the atmosphere where it suddenly becomes $$0.5$$ gravitons per mile from $$9.6$$ miles. Sally documents the gravity with the following functions:

$$g ( x ) = x - 9.6$$

$$p ( x ) = 0.5 x + 1$$

If $$x$$ represents the miles from the surface: a) Write a composite function representing the gravity $$x$$ miles from the surface.

Q:

Construct a polynomial function with the stated properties. Reduce all fractions to Fourth-degree and a single zero of $$2$$ .

Q:

At a certain time of day, a tree that is $$x$$ meters tall casts a shadow that is $$x - 35$$ meters long. If the distance from the top of the tree to the end of the shadow is $$x + 5$$ meters, what is the height, $$x$$ , of the tree?

Q:

Which type of parent function is $$f ( x ) = | x | ?$$

A. Cube root

B. Absolute value

C. Square root

D. Linear

Q:

What is the effect on the graph of $$f ( x ) = \frac { 1 } { x }$$ when it is transformed to

$$g ( x ) = \frac { 1 } { x } + 15 ?$$

A. The graph of $$f ( x )$$ is shifted $$15$$ units to the right.

B. The graph of $$f ( x )$$ is shifted $$15$$ units to the left.

C. The graph of $$f ( x )$$ is shifted $$15$$ units down.

D. The graph of $$f ( x )$$ is shifted $$15$$ units up.

Q:

While time $$t \geq 0$$ a particle moves along a straight line. Its position at time $$t$$ is given by

$$s ( t ) = 2 t ^ { 3 } - 21 t ^ { 2 } + 36 t , t \geq 0$$

where $$s$$ is measured in feet and $$t$$ in seconds.

(A) Use interval notation to indicate the time interval or union of time intervals when the particle is moving forward and backward.

Forward: $$( 1 , \frac { 7 } { 2 } ) \cup ( 6 , \infty )$$

Backward: $$( 0,1 ) \cup ( \frac { 7 } { 2 } , 6 )$$

(B) Use interval notation to indicate the time interval(s) when the particle is speeding up and slowing down.

Speeding up: $$( 1 , \frac { 7 } { 2 } ) \cup ( 6 , \infty )$$

Slowing down: $$( 0,1 ) \cup ( \frac { 7 } { 2 } , 6 )$$

Q:

You are helping a partner in your group with their problem. What mistake did they make solving the system?

$$3 x + y = 9$$

$$- 2 x + y = 4$$

Student's work when solving the second equation for $$y$$ :

$$y = 2 x + 4$$

$$- 2 x + ( 2 x + 4 ) = 4$$

$$- 2 x + 2 x + 4 = 4$$

$$4 = 4$$ The student's response is there are infinitely many solutions and this is not correct. Explain the mistake?

Q:

Given the funetion $$y = 5 x - 7$$ , how does the $$y$$ -value change as $$x$$ increases by $$1$$ ?

A. The $$y$$ -value decreases by $$7$$ .

B. The $$y$$ -value decreases by $$2$$ .

C. The $$y$$ -value increases by $$12$$ :

D. The $$y$$ -value increases by $$5$$ .

Q:

Give the slope and the $$y$$ -intercept of the line $$y = 5 x + 6 .$$ Make sure the $$y$$ -intercept is written as a coordinate. This means the $$y$$ -intercept must be in the form $$( 0 , b )$$ .

Slope

$$y$$ -intercept

Q:

Use the information given to enter an equation in standard form. Slope is $$\frac { - 5 } { 2 } ,$$ and $$( 4 , - 10 )$$ is on the line.

Q:

Enter an equation in standard form to model the linear situation.

A bathtub that holds $$48$$ gallons of water contains $$13$$ gallons of water. You begin filling it, and after $$5$$ minutes, the tub is full.

Q:

The gas station is currently charging $$\ 2.38$$ per gallon for gas. The function $$C ( n ) = 2.38 n$$ gives the cost, in dollars, to fill up your car if you pump $$n$$ gallons of gas. Your car's tank can hold a maximum of $$20$$ gallons of gas. Determine the practical domain and practical range of $$C ( n )$$ in this situation.

Q:

Which equation represents the line that passes through the points $$( - 1 , - 2 )$$ and $$( 3,10 )$$ ?

A. $$y + 2 = 3 ( x + 1 )$$ B. $$y + 1 = 3 ( x + 2 )$$

C. $$y - 2 = 3 ( x - 1 )$$ D. $$y - 1 = 3 ( x - 2 )$$

Q:

3) Consider the function, $$h ( x ) = \frac { x ^ { 2 } - 16 } { x + 6 }$$ . Where is the vertical asymptote located at? What is the behavior of the function around the vertical asymptote?

Q:

Solve the following logarithmic equation. Be sure to. reject any value of $$x$$ that is not in the domain of the original logarithmic expression. Give the exact answer.

$$\log _ { 2 } ( 2 x + 9 ) = 5$$

Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution set is __(Type an integer or a simplified fraction.)

B. There are infinitely many solutions.

C. There is no solution.

Q:

For the polynomial function $$f ( x ) = x ^ { 4 } + 10 x ^ { 3 } + 25 x ^ { 2 }$$ , answer the parts a through e.

d. Determine whether the graph has y-axis symmetry, origin symmetry, or neither, Choose the correct answer below.

A. The graph of f is symmetric about the origin.

B.The graph of f is symmetric about the y-axis.

C. The graph of f is neither symmetric about the y-axis nor symmetric about the origin.

Q:

Consider the following function, $$q ( x ) = \frac { a x ^ { m } + b x ^ { n } + 7 } { c x ^ { o } + d x ^ { p } + 10 }$$ . In this function a, $$b , c , d , m , n , o ,$$ and $$p$$ are all positive integers greater than $$1$$ . With the information given what do you know about the function?

Q:

What is the equation of the line with a slope of $$\frac { 7 } { 10 }$$ passing through the point $$( 50,28 )$$ ?

$$x + 8 y = 64$$

$$7 x - 10 y = 70$$

$$5 x + 4 y = - 63$$

$$x - 3 y = - 68$$

Q:

An employee's monthly productivity $$M$$ , in number of units produced, is found to be a function of the number $$t$$ of years of service. For a certain product, a productivity function is shown below. Find the maximum productivity and the year in which it is achieved.

$$M ( t ) = - 4 t ^ { 2 } + 200 t + 150,0 \leq t \leq 40$$

The maximum productivity is achieved in year

The maximum productivity is $$\square$$ units.

Q:

Triangle $$ABC$$ is defined by the points $$A ( 3,8 ) , B ( 7,5 )$$ , and $$C ( 2,3 )$$ . Create an equation for a line passing through point $$A$$ and perpendicular to $$\overline { BC }$$ .

Q:

In $$2012$$ , the population of a city was $$6.84$$ million. The exponential growth rate was $$1.51 \%$$ per year.

a) Find the exponential growth function. b) Estimate the population of the city in $$2018$$ . c) When will the population of the city be $$10$$ million? d) Find the doubling time. As a)

The exponential growth function is $$P ( t ) = \square$$ , where $$t$$ is in terms of the number of years since $$2012$$ and $$P ( t )$$ is the population in millions.

(Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)

Q:

Find the slope-intercept form for the equation of the line which passes through the point $$( - 3 , - 2 )$$ and the origin.

$$y = - \frac { 2 } { 3 } x - 2$$

$$y = \frac { 2 } { 3 } x$$

$$y = \frac { 3 } { 2 } x - 2$$

$$y = - \frac { 3 } { 2 } x$$

Q:

What is the equation of the line parallel to $$y = \frac { 5 } { 4 } x + ( - 3 )$$ and passes through the point $$( 9,10 )$$ ?

$$4 x - 5 y = 12$$

$$3 x + 3 y = 13$$

$$3 x + 3 y = 17$$

$$5 x - 4 y = 5$$

Q:

Which list shows the functions in order from the widest graph to the narrovest graph?

A. $$y = - 5 x , y = - 23 x , y = 56 x , y = 8 x$$

B. $$y = - 23 x , y = 56 x , y = - 5 x , y = 8 x$$

C. $$y = 56 x , y = - 23 x , y = 8 x , y = - 5 x$$

D. $$y = 8 x , y = 56 x , y = - 23 x , y = - 5 x$$

Q:

A line has the two endpoints $$A ( - 26,7 )$$

$$B ( 16 , - 11 )$$ and a midpoint of $$C$$ . What is the equation of the perpendicular bisector in standard form? The equation is given by $$A x + B y = C$$ where

$$A =$$ and $$C =$$

* Remember, when writing an equation in standard form you must simplify until the x-coefficient is positive.

Q:

A preimage includes a line segment with a length of $$x$$ units and a slope of $$m$$ units. The preimage is dilated by a scale factor of $$n$$ . The length of the corresponding line segment in the image is ___units. The slope of the corresponding line segment in the image is ___

Q:

What is the equation for a line with a slope of $$\frac { 3 } { 2 }$$

that passes through the point $$( 5,10 )$$ ?

$$2 x - 3 y = 70$$

$$3 x - 2 y = - 5$$

$$4 x + 8 y = - 51$$

$$8 x + 4 y = 2$$

Q:

The line segment $$A B$$ has the endpoints $$A ( 1,12 )$$ and $$B ( - 9 , - 8 )$$ . Pont $$C$$ partitions the line at a ratio of $$2 : 3$$ . What are the coordinates of point $$C$$ ? The coordinates are given by $$( x , y )$$ where

$$x = \quad ,$$ and $$y =$$

Q:

The graph of which quadratic function has vertex $$( - 3,2 )$$ and passes through the point $$( - 1 , - 10 )$$ ?

A. $$y = - 3 \times 2 - 18 \times - 25$$

B. $$y = - 12 \times 2 + 2 x + 5$$

C. $$y = x 2 + 6 x + 11$$

D. $$y = x 2 - 4 x - 25$$

Q:

How does the graph of $$y = x + 3$$ differ from the graph of $$y = x - 5$$ ?

A. The graph of $$y = x + 3$$ is wider than the graph of $$y = x - 5$$

B. The graph of $$y = x + 3$$ is narrower than the graph of $$y = x - 5$$

C. The graph of $$y = x + 3$$ is $$8$$ units above the graph of $$y = x - 5$$

D. The graph of $$y = x + 3$$ is $$2$$ units below the graph of $$y = x - 5$$

Q:

Write an equation of the line passing through the point $$( 6 , - 2 )$$ that is parallel to the line $$y = 4 x - 11$$ . a $$y = - \frac { 1 } { 4 } x - 2$$

$$y = 4 x - 2$$

$$y = 4 x - 26$$

$$y = - \frac { 1 } { 4 } x - 26$$

Q:

Suppose that $$f ( x ) = 7 x - 5$$ and $$g ( x ) = - 3 x + 5$$

(a) Solve $$f ( x ) = 0$$

(b) Solve $$f ( x ) > 0$$

(c) Solve $$f ( x ) = g ( x )$$

(d) Solve $$f ( x ) \leq g ( x )$$

(e) Graph $$y = f ( x )$$ and $$y = g ( x )$$ and find the point that represents the solution to the equation $$f ( x ) = g ( x )$$

Q:

Find the slope and $$y$$ -intercept of the line whose equation is given.

$$4 x - 3 y = 15$$

Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is B. The slope is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept is B. There is no $$y$$ -intercept.

Q:

The cost $$C$$ , in dollars, of renting a moving truck for a day is given by the function $$C ( x ) = 0.20 x + 45$$ , where $$x$$ is the number of miles driven.

(a) What is the cost if a person drives $$x = 240$$ miles?

(b) If the cost of renting the moving truck is $$\ 180$$ , how many miles did the person drive?

(c) Suppose that a person wants the cost to be no more than $$\ 150$$ . What is the maximum number of miles the person can drive?

(d) What is the implied domain of $$C$$ ?

(e) Interpret the slope. (f) Interpret the $$y$$ -intercept.

Q:

Which equation represents a line which is parallel to the line $$x + 4 y = - 20$$ ?

$$y = 4 x + 7$$

$$y = \frac { 1 } { 4 } x - 7$$

$$y = - 4 x + 1$$

$$y = - \frac { 1 } { 4 } x - 1$$

Q:

Find the Riemann sum $$S _ { 4 }$$ for the following information. Round your answer to the nearest hundredth.

$$f ( x ) = 64 - x ^ { 2 } ; [ a , b ] = [ - 8 , - 4 ] ; n = 4 , c _ { 1 } = - 7.5 , c _ { 2 } = - 6.5 , c _ { 3 } = - 5.5 , c _ { 4 } = - 4.5$$

AnswerHow to enter your answer (opens in new window) $$2$$ Points Keyboard Shortcuts

$$S _ { 4 } =$$

Q:

Find an equation for the line that Passes through the Points

$$( - 4,1 )$$ and $$( 6 , - 3 )$$

Q:

Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the $$y$$ -axis, the origin, or neither

$$f ( x ) = x ^ { 3 } - 3 x$$

Determine whether the function is even, odd, or neither. Choose the correct answer below.

neither

odd

even

Determine whether the graph of the function is symmetric with respect to the y-axis, the origin, or neither. Select all that apply.

neither

y-axis

origin

Q:

Find the slope and $$y$$ -intercept for the following equation.

$$y = \frac { 2 } { 5 } - 3 x$$

$$b = \square$$

$$b = \square$$

Q:

Find the slope and $$y$$ -intercept for the following equation.

$$y = 3 x$$

$$m = \square$$

$$b = \square$$

Q:

Consider the Quadratic function $$f ( x ) = x ^ { 2 } - 5 x - 6$$ .

Its vertex is(___,___)

Its smallest $$x$$ -intercept is $$x =$$ ___

Its $$y$$ -intercept is $$y =$$ ___

Note: Enter $$x$$ and $$y$$ intercepts as a single number.

Q:

Find the slope and $$y$$ -intercept for the line. Then write the equation of the line in slope-intercept form.

Q:

Suppose that the functions $$q$$ and $$r$$ are defined as follows.

$$q ( x ) = 2 x$$

$$r ( x ) = x ^ { 2 } - 1$$

Find the following.

$$( r \cdot q ) ( - 2 ) =$$

$$( q \cdot r ) ( - 2 ) =$$

Q:

Which equation represents a line which is parallel to the line $$y = \frac { 1 } { 2 } x + 3$$ ?

$$y - 2 x = - 5$$

$$2 x + y = - 6$$

$$x - 2 y = 2$$

$$x + 2 y = 4$$

Q:

Which equation represents a line which is perpendicular to the line $$y = - \frac { 1 } { 8 } x + 3$$ ?

$$8 x + y = 6$$

$$x - 8 y = 40$$

$$x + 8 y = - 40$$

$$y - 8 x = - 2$$

Q:

The graph of a proportional relationship contains the point $$( 20,4 )$$

What is the corresponding equation?

Enter your answer as a fraction in simplest form by filling in the boxes.

$$y = \frac { \square } { \square } x$$

Q:

Which equation represents a line which is perpendicular to the line $$4 x - 3 y = 12$$ ? $$y = - \frac { 3 } { 4 } x + 4$$

$$y = \frac { 3 } { 4 } x - 8$$

$$y = - \frac { 4 } { 3 } x + 3$$

$$y = \frac { 4 } { 3 } x + 2$$

Q:

Do the values in the table represent a proportional relationsnip?

Select from the drop-down menu to correctly complete the statement.

All of the $$y$$ -values ___a constant multiple of the corresponding $$x$$ -values, so the relationship ____

Q:

If an object is propelled upward from a height of $$112$$ feet at an initial velocity of $$96$$ feet per second, then its height $$h$$ after $$t$$ seconds is given by the equation

$$h = - 16 t ^ { 2 } + 96 t + 112$$ . After how many seconds does the object hit the ground?

$$6 sec$$

$$7 sec$$

$$11 sec$$

$$3.5 sec$$

Q:

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution.

$$5 ^ { x - 2 } = 246$$

The solution set expressed in terms of logarithms is

(Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression. Use In for natural logarithm and log for common logarithm.)

Q:

Tell the maximum number of zeros that the polynomial function may have. Then use Descartes' Rule of Signs to determine how many positive and how many negative $$6.25 \% , 2$$ of $$32$$ real zeros the polynomial function may have. Do not attempt to find the zeros.

$$f ( x ) = 8 x ^ { 7 } + x ^ { 3 } - x ^ { 2 } + 8$$

What is the maximum number of zeros that this polynomial function can have?

Q:

A culture of bacteria grows according to the continuous growth model

$$B = f ( t ) = 700 e ^ { 0.034 t }$$

where $$B$$ is the number of bacteria and $$t$$ is in hours. Find

$$f ( 0 ) =$$

To the nearest whole number, find the number of bacteria after $$8$$ hours. To the nearest tenth of an hour, determine how long it will take for the population to grow to $$1300$$ bacteria.