Question

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

A. The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units to the right
B. The graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units down
C. The graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units to the right
D. The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down

Answer 1

D

Explanation:

The statement that best compares the graph G(x) with the graph of F(x) is:

D. The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down.

This is because the equation G(x) = 2x^2 - 5 can be written as G(x) = 2(x^2) - 5, which means the graph of G(x) is the graph of F(x) (x^2) stretched by a factor of 2 vertically, and shifted down by 5 units.

A. The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units to the right is incorrect, because there is no shift horizontally in the equation.

B. The graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units down is incorrect, because the graph is stretched not compressed.

C. The graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units to the right is incorrect, because the graph is stretched not compressed, and there is no shift horizontally in the equation.

Answer 2

I believe the correct answer from the choices listed above is option D. The graph G(x) as compared to the graph of F(x) would be that the graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down. 2 is a stretch factor and -5 is the shift downwards of the graph. Hope this answers the question.