Answer:The graph of [tex]G(x)[/tex] is the graph of [tex]F(x)[/tex] compressed vertically.
Step-by-step explanation:
Given that [tex]F(x)=x^{2}[/tex] and [tex]G(x)=\frac{2}{3}x^{2}[/tex]
[tex]F(x)[/tex] is always positive because [tex]x^{2}[/tex] is always positive.
[tex]G(x)[/tex] is always positive because [tex]\frac{2}{3}x^{2}[/tex] is always positive.
So,both are always positive.
So,there is no flipping over x-axis.
In [tex]F(x)[/tex],the height of a point at [tex]x_{0}[/tex] is [tex]x_{0}^{2}[/tex]
In [tex]G(x)[/tex],the height of a point at [tex]x_{0}[/tex] is [tex]\frac{2}{3}x_{0}^{2}[/tex]
So,height of any point has less height in [tex]G(x)[/tex] than [tex]F(x)[/tex]
So,the graph of [tex]G(x)[/tex] is the graph of [tex]F(x)[/tex] compressed vertically.
