Answer: The graph of g(x) is the graph of f(x) compresed vertically.
Step-by-step explanation:
Given the parent function [tex]f(x)^2[/tex], there are some transformations rules:
If [tex]f(x)=a(x^2)[/tex] when [tex]a>1[/tex], then it is stretched vertically.
If [tex]f(x)=a(x^2)[/tex] when [tex]0<a<1[/tex], then it is compresed vertically.
If [tex]f(x)=(ax)^2[/tex] when [tex]0<a<1[/tex], then it is stretched horizontally.
If [tex]f(x)=(ax)^2[/tex] when [tex]a>1[/tex], then it is compresed horizontally.
In this case for [tex]g(x)=\frac{2}{5}x^2[/tex], it has the form [tex]f(x)=a(x^2)[/tex] and [tex]0<a<1[/tex], then the graph of g(x) is the graph of f(x) compresed vertically.
