Question

Function g can be thought of as a scaled version of f(x) = x².

f
-5 -4 -3
Y
5.
4+
3.
2-
1
234
-4+
-5
Write the equation for g(x).
g(x) =
345
(2,-1)
B

Answer 1

g(x) = -1/4x²

Explanation:

Given f(x) = x² and point (2, -1) on the graph of g(x), which is a scaled version of f(x), you want the equation for g(x).

Scale factor

The scale factor k will satisfy ...

g(x) = k·f(x)

g(2) = k·f(2) . . . . . . true at the given point

-1 = k·2² = 4k . . . . use the coordinates of the given point

k = -1/4 . . . . . . . . . divide by 4

The equation of g(x) is ...

g(x) = -1/4x²