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The graph of the absolute value parent function, [tex]$f(x)=|x|$[/tex], is stretched horizontally by a factor of 5 to create the graph of [tex]$g(x)$[/tex]. What function is [tex][tex]$g(x)$[/tex][/tex]?

A. [tex]$g(x)=5|x|$[/tex]
B. [tex]$g(x)=|x+5|$[/tex]
C. [tex]$g(x)=\left|\frac{1}{5} x\right|$[/tex]
D. [tex][tex]$g(x)=|5 x|$[/tex][/tex]

Sagot :

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To determine the function [tex]\( g(x) \)[/tex] that results from horizontally stretching the parent function [tex]\( f(x) = |x| \)[/tex] by a factor of 5, we need to understand how horizontal stretching affects the function.

When a function [tex]\( f(x) \)[/tex] is horizontally stretched by a factor of [tex]\( a \)[/tex], the transformation is done by multiplying the variable [tex]\( x \)[/tex] by [tex]\( \frac{1}{a} \)[/tex] inside the function.

In this problem, the horizontal stretch factor is 5. Therefore, we need to multiply [tex]\( x \)[/tex] by [tex]\( \frac{1}{5} \)[/tex] within the absolute value function to get the desired transformation.

The new function [tex]\( g(x) \)[/tex] would then be:
[tex]\[ g(x) = \left| \frac{1}{5} x \right| \][/tex]

Thus, the function [tex]\( g(x) \)[/tex] that represents the graph of the absolute value parent function [tex]\( f(x) = |x| \)[/tex] stretched horizontally by a factor of 5 is:

C. [tex]\( g(x) = \left| \frac{1}{5} x \right| \)[/tex]
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