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]
