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.

Question

Jax Riggs

Mathematics

11 August, 18:05

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.

+4

Answers (1)

Know the Answer?

Karen Burns · 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
-1
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.