Answer:
g(x) is a dilation of function f(x), and [tex]g(x) = \frac{1}{4}x^2[/tex]
Step-by-step explanation:
Function f is [tex]f(x) = x^2[/tex]
So:
When [tex]x = 0, f(x) = 0[/tex]
When [tex]x = 1, f(x) = 1[/tex]
When [tex]x = 2, f(x) = 4[/tex]
When [tex]x = 3, f(x) = 9[/tex]
Now
For function g, looking at the graphic, we have that:
When [tex]x = 0, g(x) = 0[/tex]
When [tex]x = 2, g(x) = 1[/tex]
When [tex]x = 3, g(x) = 2.5[/tex]
That is, g(x) is a fourth of f(x).
This means that we have a dilation by a factor of 1/4, so [tex]g(x) = \frac{1}{4}x^2[/tex]
