Answer:
The correct option is C.
Step-by-step explanation:
The given function is
[tex]f(x)=x^2[/tex]
From the given graph it is clear that the vertex of f(x) and g(x) are same, i.e.,(0,0). But the graph of g(x) compressed vertically.
[tex]g(x)=kf(x)[/tex]
If k>1, then graph of g(x) stretched vertically and if k<1, then graph of g(x) compressed vertically.
[tex]g(x)=kx^2[/tex]
The graph of g(x) passing through the point (2,2).
[tex]2=k(2)^2[/tex]
[tex]2=4k[/tex]
[tex]k=\frac{1}{2}[/tex]
The value of k is 1/2. The function g(x) is
[tex]g(x)=\frac{1}{2}x^2[/tex]
Therefore, option C is correct.
