Given:
The parent function is:
[tex]f(x)=x^2[/tex]
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,
[tex]g(x)=kf(x)[/tex]
Where, k is the stretch factor.
It can be written as:
[tex]g(x)=kx^2[/tex] ...(i)
The graph of g(x) passes through the point (3,3). Putting [tex]g(x)=3,x=3[/tex] in (i), we get
[tex]3=k(3)^2[/tex]
[tex]3=k(9)[/tex]
[tex]\dfrac{3}{9}=k[/tex]
[tex]\dfrac{1}{3}=k[/tex]
Putting [tex]k=\dfrac{1}{3}[/tex] in (i), we get
[tex]g(x)=\dfrac{1}{3}x^2[/tex]
Therefore, the correct option is D.
