Question

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

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

$3=k(3)^2$

$3=k(9)$

$\dfrac{3}{9}=k$

$\dfrac{1}{3}=k$

Putting $k=\dfrac{1}{3}$ in (i), we get

$g(x)=\dfrac{1}{3}x^2$

Therefore, the correct option is D.