Answer:
[tex]g(x)=\frac{1}{8} x^{2}[/tex]
Step-by-step explanation:
Expansions and compressions are transformations that change the length or width of the graph of a function. The general form of the graph of a function expands or compresses vertically or horizontally. Expansions and compressions are considered non-rigid transformations.
Vertical compression:
[tex]y=kf(x)[/tex]
- If k>0 the graph of f (x) is vertically stretched by a factor of k.
- If k<0 the vertical stretch is followed by a reflection across the x-axis.
- If 0<k<1 the graph is f (x) vertically compressed by a factor of 1/k.
So, if [tex]f(x)=x^{2}[/tex] is vertically compressed by a factor of 8. Hence, using the previous information, we can conclude that the equation of [tex]g(x)[/tex] is:
[tex]g(x)=\frac{1}{8} x^{2}[/tex]
I attached you the graphs.
