Notice that the vertex of the graph of g(x) is at (0,0); therefore, no translation was applied to f(x). On the other hand, the graph of g(x) goes through (2,1) rather than (1,1); therefore, g(x) is a vertical compression of f(x).
In general, a vertical compression is given by the formula below (given a function h(x))
[tex]h(x)\rightarrow ah(x);0Then, in our case,[tex]g(x)=a*f(x)[/tex]
To determine a, remember that the graph of g(x) includes the point (2,1); then,
[tex]\begin{gathered} 1=g(2)=a*f(2)=a*2^2 \\ \Rightarrow1=a*4 \\ \Rightarrow a=\frac{1}{4} \\ \Rightarrow g(x)=\frac{1}{4}f(x) \end{gathered}[/tex]
The answer is 'g(x) is a vertical compression of function f. g(x)=1/4*x^2'
