Question

F(x) = x2 What is g(x)?

5+
[f(x)
V
g(x)
(3, 3)
-5-
A. g(x) = 6x2
O B. 90%)-

Answer 1

Given:

The parent function is:

`f(x)=x^2`

The graphs of f(x) and g(x) are given.

The graph of g(x) passes through the point (3,3).

To find:

The function g(x).

Solution:

From the given graph, it is clear that the graph of f(x) compressed vertically to get the graph of g(x). So,

`g(x)=kf(x)`

Where, k is the stretch factor.

It can be written as:

`g(x)=kx^2` ...(i)

The graph of g(x) passes through the point (3,3). Putting
`g(x)=3,x=3` in (i), we get

`3=k(3)^2`

`3=k(9)`

`(3)/(9)=k`

`(1)/(3)=k`

Putting
`k=(1)/(3)` in (i), we get

`g(x)=(1)/(3)x^2`

Therefore, the correct option is D.