Question

h(x) = x³ - 2
parent: ____
transformations: ____

for problems 10 – 14, given the parent function and a description of the transformation, write the equation of the transformed function, f(x).

1. absolute value—vertical shift down 5, horizontal shift right 3. ____
2. linear—vertical shift up 5. ____
3. square root —vertical shift down 2, horizontal shift left 7. ____
4. quadratic— horizontal shift left 8. ____
5. quadratic—vertex at (-5, -2). ____

for problems 15 & 16, circle the graph that best represents the given function.

1. f(x) = x² - 2?

a. graph b. graph c. graph d. graph

1. g(x) = |x+3|?

a. graph b. graph c. graph d. graph
page |3

Explanation:

Problem 10

Step1: Identify parent function

The parent function for absolute value is \( y = |x| \).

Step2: Apply horizontal shift

A horizontal shift right 3 units replaces \( x \) with \( x - 3 \), so we get \( y = |x - 3| \).

Step3: Apply vertical shift

A vertical shift down 5 units subtracts 5 from the function, so \( y = |x - 3| - 5 \).

Step1: Identify parent function

The parent function for linear is \( y = x \).

Step2: Apply vertical shift

A vertical shift up 5 units adds 5 to the function, so \( y = x + 5 \).

Step1: Identify parent function

The parent function for square root is \( y=\sqrt{x} \).

Step2: Apply horizontal shift

A horizontal shift left 7 units replaces \( x \) with \( x + 7 \), so \( y=\sqrt{x + 7} \).

Step3: Apply vertical shift

A vertical shift down 2 units subtracts 2 from the function, so \( y=\sqrt{x + 7}-2 \).

Answer:

\( f(x)=|x - 3| - 5 \)

Problem 11