Question

Suppose fx) = x² and g(x) = 1/3)² Which statement best compares the graph of g(x) with the graph of f(x)?

a. g(x) is a horizontal compression of f(x).
b. g(x) is a vertical compression of f(x).
c. g(x) is a horizontal stretch of f(x).
d. g(x) is a vertical stretch of f(x).

Answer 1

The graph of g(x) = (1/3x)² is a horizontal stretch of the graph f(x) = x², because the x-value is effectively multiplied by 1/3 before squaring, requiring a larger x-value to achieve the same y-value as f(x).

Correct option is c.

Step-by-step explanation:

When comparing the graph of g(x) = (1/3x)² to the graph of f(x) = x², it's important to understand the effect of the coefficient 1/3 in g(x).

In the function g(x), you multiply the input x by 1/3 before squaring it.

This results in a horizontal stretch of the original graph f(x), because for a given y-value, the x-value must be greater to compensate for the multiplication by 1/3. Therefore, the correct answer is that g(x) is a horizontal stretch of f(x),

which makes option c the correct choice.