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)

Question

asked Feb 28, 2020 70.2k views

2 Answers

Master Yoda · Answer 1 · 2020-03-01T11:22:04+0000

Answer:

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

$If the parent function f(x)=\root(3)(x) is transformed to g(x)=\root(3)(x+2-4), which-example-1$

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

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

Ryon · Answer 2 · 2020-03-05T06:40:59+0000

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.