The graphs for the functions \( f ( x ) = \sqrt { x } - 3 \) and \( g ( x ) = \sqrt { x - 3 } \) are shown in the graph below.
Describe the transformations of a parent function to obtain the graphs of
\( f ( x ) \) and \( g ( x ) \) .
Question
Answer
f(x) - shift the parent graph 3 units downward.
g(x) - shift the parent graph 3 units rightwards
Related Questions
Q:
It takes \( 8 \) minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes \( 5 \) minutes to fill the pool. Which equation can be used to determine r; the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
\( \frac { 5 } { 8 } + 5 r = 8 \)
\( \frac { 5 } { 8 } + 5 r = 1 \)
\(5 ( \frac { 5 } { 8 } ) = r \)
\( \frac { 5 } { 8 } = 5 r\)
Q:
Mike and Jamal are \( 9 \) miles apart, and are planning to meet up. Mike is walking at an average speed of \( 3 \) miles per hour to meet Jamal. Jamal is driving at an average speed of \( 25 \) miles per hour to meet Mike.
Which equation can be used to find \( t \) , the time it takes for Mike and Jamal to meet?
\(25 t - 3 t = 0 \)
\( 25 t - 3 t = 9 \)
\( 25 t + 3 t = 1 \)
\( 25 t + 3 t = 9\)
Q:
On a map, each inch represents \( 6.5 \) miles. What is the distance represented by \( 6 \) inches?
Step \( 1 \) of 2: Set up the proportion for the word problem. Use \( x \) as the unknown variable.
Q:
Ali's latest photo got \( 42 \) likes. This is \( 3 \) times as many likes as Kate's latest photo. How many likes did Kate's photo get? Select the correct solution method below, using \( x \) to represent Kate's likes.
A. \( 3 x = 42 \) . Divide both sides by \( 3 \) . Kate's photo got \( 14 \) likes.
B. \( \frac { x } { 3 } = 42 \) . Multiply both sides by \( 3 \) . Kate's photo got \( 126 \) likes.
C. \( x + 3 = 42 \) . Subtract \( 3 \) from both sides. Kate's photo got \( 39 \) likes.
D. \( x - 3 = 42 \) . Add \( 3 \) to both sides. Kate's photo got \( 45 \) likes.
Q:
Ali's latest photo got \( 42 \) likes. This is \( 3 \) times as many likes as Kate's latest photo. How many likes did Kate's photo get? Select the correct solution method below, using \( x \) to represent Kate's likes.
A. \( 3 x = 42 \) . Divide both sides by \( 3 \) . Kate's photo got \( 14 \) likes.
B. \( \frac { x } { 3 } = 42 \) . Multiply both sides by \( 3 \) . Kate's photo got \( 126 \) likes.
C. \( x + 3 = 42 \) . Subtract \( 3 \) from both sides. Kate's photo got \( 39 \) likes.
D. \( x - 3 = 42 \) . Add \( 3 \) to both sides. Kate's photo got \( 45 \) likes.