Respuesta :
Answer:
As per the statement given that [tex]F(x) = x^3[/tex] and [tex]G(x) = -2x^3-7[/tex]
⇒ Let the parent function be [tex]F(x) = x^3[/tex]
Vertically Stretch: If y =f(x) , then y = a f(x) gives a vertical stretch if a> 1.
Rotation about x -axis: [tex](x, y) \rightarrow (x, -y)[/tex]
Shifting down: To shift a graph down some units c, we will be subtracting outside the function: y= f(x)-c.
Just Multiplying the parent function by 2 means you are stretching it vertically,
i,e F(x) =[tex]x^3 \rightarrow \text{Vertically stretch by 2} \rightarrow 2x^3[/tex]
adding the minus sign means you are flipping or rotating it about the x-axis
i,e [tex]2x^3 \rightarrow \text{Rotation about x- axis} \rightarrow -2x^3[/tex]
and subtracting 7 means you are moving it down by 7 units
[tex]-2x^3 \rightarrow \text{Shifted down by 7 units} \rightarrow -2x^3-7[/tex] =G(x)
Therefore, the statement best compare the graph G(x) with the graph of F(x)
the graph of G(x) is the graph of F(x) stretched vertically by 2 units, flipped over the x-axis, and shifted 7 units down.
