Question

Suppose that f(x)=x^2 and g(x)=2/5x^2. How does the graph of g(x) compare with the graph of f(x)?

Answer 1

Answer: The graph of g(x) is the graph of f(x) compresed vertically.

Step-by-step explanation:

Given the parent function $f(x)^2$, there are some transformations rules:

If $f(x)=a(x^2)$ when $a>1$, then it is stretched vertically.

If $f(x)=a(x^2)$ when $0$, then it is compresed vertically.

If $f(x)=(ax)^2$ when $0$, then it is stretched horizontally.

If $f(x)=(ax)^2$ when $a>1$, then it is compresed horizontally.

In this case for $g(x)=\frac{2}{5}x^2$, it has the form $f(x)=a(x^2)$ and $0$, then the graph of g(x) is the graph of f(x) compresed vertically.