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)?

Answer 1

Answer:

A)

Step-by-step 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

ANSWER

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.