Question

Suppose that F(x) = x3 and G(x) = -2x3 - 7. 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) compressed vertically, flipped over the x-axis, and shifted 7 units to the right.
B. The graph of G(x) is the graph of F(x) compressed vertically, flipped over the x-axis, and shifted 7 units down.
C. The graph of G(x) is the graph of F(x) stretched vertically, flipped over the x-axis, and shifted 7 units down.
D. The graph of G(x) is the graph of F(x) stretched vertically, flipped over the x-axis, and shifted 7 units to the right.

Answer 1

Reflections:
 A reflection or turning is the mirror image of a figure. It can also be said that it is the turning of points and graphs around the axes.
 To graph y = -f (x), reflect the graph of y = f (x) on the x-axis. (Vertical reflection)
 Resulting:
 -x3
 Expansions and Compressions:
 Expansions and compressions are transformations that change the length or width of the graph of a function. The general form of the graph of a function expands or compresses vertically or horizontally.
 To graph y = a f (x)
 If a> 1, the graph of y = f (x) is expanded vertically by a factor a. 
 Resulting:
 -2x3
 Displacements (Translations)Translations are transformations that change the position of the graph of a function.
 Suppose that k > 0
 To graph y = f (x) - k, move the graph of k units down.
 Resulting:
 G (x) = -2x3 - 7
 Answer:
 C. The graph of G (x) is the graph of F (x) stretched vertically, reflected over the x-axis, and shifted 7 units down.