Question

Suppose that F(x) = x^2 and G(x) = 2/3x^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) compressed vertically.
B.) the graph of G(x) is the graph of F(x) stretched vertically and flipped over the x-axis.
C.) the graph of G(x) is the graph of F(x) stretched vertically.
D.) the graph of G(x) is the graph of F(x) compressed vertically and flipped over the x-axis

Answer 1

Multiplying a function by a number that when squared is less than one, compresses the graph vertically by a factor equal to the coefficient.

In this case (2/3)^2=4/9 and 4/9<1 so the graph of G(x) is the graph of F(x) compressed vertically.

Answer 2

The statement which best compares the function F(x) and G(x) is that the graph of G(x) is the graph of F(x) stretched vertically.

Explanation:

Since the difference between the two functions is in the coefficent which multiplies the square function, 1 and 2/3 respectively in F(x) and G(x). So, as the coefficient are positive and is minor for G(x) than for F(x), the values for G(x) will be smaller and thus the graph of G(x) would be below the graph of F(x). Therefore the graph for G(x) is it compressed vertically respect to F(x). The explanation here is ore understandable by looking at the illustration attached.