Questions: Question 5 (1 point) Which of the following represents a vertical stretch to the parent function f(x)=x ? g(x)=-x g(x)=(1/3) x g(x)=3x g(x)=-x g(x)=(1/3)x g(x)=3 x

Transcript text: Question 5 (1 point) Listen Which of the following represents a vertical stretch to the parent function $f(x)=|x| ?$ $g(x)=|-x|$ $g(x)=\left|\frac{1}{3} x\right|$ $g(x)=3|x|$ $g(x)=-|x|$ $g(x)=\frac{1}{3}|x|$ $g(x)=|3 x|$

Solution

Solution Steps

To determine which function represents a vertical stretch of the parent function $ f(x) = |x| $, we need to identify the transformation that multiplies the output of the function by a factor greater than 1. A vertical stretch occurs when the function is multiplied by a constant greater than 1.

Step 1: Identify the Transformation

Step 2: Analyze Each Function

Given the functions:

$ g(x) = |-x| $
$ g(x) = \left|\frac{1}{3} x\right| $
$ g(x) = 3|x| $
$ g(x) = -|x| $
$ g(x) = \frac{1}{3}|x| $
$ g(x) = |3x| $

We analyze each to see which one is of the form $ g(x) = c|x| $ with $ c > 1 $.

Step 3: Determine the Vertical Stretch

The function $ g(x) = 3|x| $ is of the form $ g(x) = c|x| $ where $ c = 3 $. Since $ 3 > 1 $, this represents a vertical stretch of the parent function $ f(x) = |x| $.