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y=3x-6

Algebra Calculus Trigonometry Matrix

Question

y=3x-6

Function

m=3

Evaluate

y=3x-6

Solution

m=3

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Find the slope

Find the inverse

Evaluate the derivative

Find the domain

\text{Find the }x\text{-intercept/zero}

Find the y-intercept

Find the range

Find the vertical asymptotes

Find the horizontal asymptotes

Determine if even, odd or neither

Find the stationary points

Testing for symmetry

\textrm{Not symmetry with respect to the origin}

Evaluate

y=3x-6

\text{To test if the graph of }y=3x-6\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}

-y=3\left(-x\right)-6

Simplify

-y=-3x-6

Change the signs both sides

y=3x+6

Solution

\textrm{Not symmetry with respect to the origin}

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Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Solve the equation

x=\frac{y+6}{3}

Evaluate

y=3x-6

Swap the sides of the equation

3x-6=y

Move the constant to the right-hand side and change its sign

3x=y+6

Divide both sides

\frac{3x}{3}=\frac{y+6}{3}

Solution

x=\frac{y+6}{3}

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Rewrite the equation

r=-\frac{6}{\sin\left(\theta \right)-3\cos\left(\theta \right)}

Evaluate

y=3x-6

Move the expression to the left side

y-3x=-6

\text{To convert the equation to polar coordinates,substitute }x\text{ for }r\cos\left(\theta \right)\text{ and }y\text{ for }r\sin\left(\theta \right)

\sin\left(\theta \right)\times r-3\cos\left(\theta \right)\times r=-6

Factor the expression

\left(\sin\left(\theta \right)-3\cos\left(\theta \right)\right)r=-6

Solution

r=-\frac{6}{\sin\left(\theta \right)-3\cos\left(\theta \right)}

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