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Function
g can be thought of as a scaled version of
f(x)=|x|.
What is the equation for
g(x) ?
Choose 1 answer:

g(x)=(|x|)/(3)

g(x)=|x+4|

g(x)=|x|+4

g(x)=3|x|

Function $g$ can be thought of as a scaled version of $f(x)=|x|$ . $\newline$ What is the equation for $g(x)$ ? $\newline$ Choose $1$ answer: $\newline$ $g(x)=\frac{|x|}{3}$ $\newline$ $g(x)=|x+4|$ $\newline$ $g(x)=|x|+4$ $\newline$ $g(x)=3|x|$

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Evaluate a nonlinear function

Full solution

Q. Function

g

can be thought of as a scaled version of

f(x)=|x|

.

\newline

What is the equation for

g(x)

?

\newline

Choose

1

answer:

\newline

g(x)=\frac{|x|}{3}

\newline

g(x)=|x+4|

\newline

g(x)=|x|+4

\newline

g(x)=3|x|

Given Information: We are given that $g$ can be thought of as a scaled version of $f(x)=|x|$ . This means that $g(x)$ will be a multiple of $f(x)$ . The options given are $g(x)=\frac{|x|}{3}$ , $g(x)=|x+4|$ , $g(x)=|x|+4$ , and $g(x)=3|x|$ . We need to identify which of these represents a scaling of $f(x)$ .
Identifying Scaling: The option $g(x)=\frac{|x|}{3}$ represents a scaling of $f(x)$ by a factor of $\frac{1}{3}$ , which means the graph of $g(x)$ would be compressed vertically compared to $f(x)$ .
Option Analysis: The option $g(x)=|x+4|$ represents a horizontal shift of the graph of $f(x)$ by $4$ units to the left, not a scaling.
Option $1$ : Scaling by $1$ / $3$ : The option $g(x)=|x|+4$ represents a vertical shift of the graph of $f(x)$ by $4$ units upwards, not a scaling.
Option $2$ : Horizontal Shift: The option $g(x)=3|x|$ represents a scaling of $f(x)$ by a factor of $3$ , which means the graph of $g(x)$ would be stretched vertically compared to $f(x)$ . This is the correct representation of a scaled version of $f(x)$ .

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