Question

Suppose that F(x)=x^3 and G(x)= -5x^3+2. Which statement best compares the graph of G(x) with the graph of F(x)?

A. The graph of G(x) is the graph of F(x) stretched vertically, flipped over the x-axis, and shifted 2 units to the left.

B. The graph of G(x) is the graph of F(x) compressed vertically, flipped over the x-axis, and shifted 2 units up.

C. The graph of G(x) is the graph of F(x) stretched vertically, flipped over the x-axis, and shifted 2 units up.

D. The graph of G(x) is the graph of F(x) compressed vertically, flipped over the x-axis, and shifted 2 units to the left.

Answer 1

If the parent function f(x)=x^3, then
g(x)=a f(x-h) + k
will stretch the parent function by a factor of a, translates to the right by h (h>=0) and translates up k units (k>0).
For h,k negative, translation moves in the opposite direction.
Also,
a>1  is a stretch,
0<a<1 is a shrink (reduction)
-1<a<0 is a shrink followed by a reflection (flip) about the x-axis
a<-1 is a stretch by a factor of |a|, followed by a reflection (flip) about the x-axis.
Here a=-5, h=0, k=2.

Answer 2

A. The graph of G(x) is the graph of F(x) stretched vertically, flipped over the x-axis, and shifted 2 units to the left.

What is the Parent function?

If the parent function $f(x)=x^3$, then

g(x)=a f(x-h) + k

will stretch the parent function by a factor of a, translates to the right by h (h>=0), and translates up k units (k>0).

For h,k negative, translation moves in the opposite direction.

Also,

a>1  is a stretch,

0<a<1 is a shrink (reduction)

-1<a<0 is a shrink followed by a reflection (flip) about the x-axis

a<-1 is a stretch by a factor of |a|, followed by a reflection (flip) about the x-axis.

Here a=-5, h=0, k=2.

To learn more about F(x) and G(x), refer to:

https://brainly.com/question/9921945

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