Question

If the parent function f(x)=\root(3)(x) is transformed to g(x)=\root(3)(x+2-4), which is the graph of g(x)?

(Photos of graphs included)
(15 points)

Answer 1

A)

Explanation:

First we will graph th parent function which is a cube root and we can see it in the attachment #1.

In this excercise there are two types of transformations of the parent function:

`f(x)=\sqrt[3]{x}`

First:

`f(x+b)` shifts the function b units to the left.(Attachment #2 )

`f(x)=\sqrt[3]{x+2}`

`b=2`

Second:

`f(x)-c` shifts the function c units downward. (Attachment #3)

`f(x)=\sqrt[3]{x+2}+4`

`c=4`

Answer 2

A.

EXPLANATION

The parent function is

`f(x) = \sqrt[3]{x}`

This function is transformed to obtain

`g(x) = \sqrt[3]{x + 2} - 4`

The +2 is a horizontal translation, that shifts the graph of the parent function to the left by 2 units.

The -4 is a vertical translation, that shifts the graph of the parent function down by 4 units.

The correct option is A.