Question

suppose that F(x)=x^2 and G(x)=(1/4x)^2. Which statement best compares the graph of g(x) with the graph of f(x)

Answer 1

g(x) is the image of f(x) after stretched horizontally by scale factor = 4

Explanation:

The statement that best compares the graph of g(x) with the graph of f(x) says g(x) is the image of f(x) after stretched horizontally by scale factor = 4 because:

Given the function

f(x) = x² and g(x) = (1/4x)² the image of f(x) after one transformation.

The transformation shows that g(x) stretches away from y-axis.

Since the transformation is stretched horizontally. So g(x) is the image of f(x) after stretched horizontally by scale factor (I.e. by 1).

Then we use the scale factor to divide g(x)

1 ÷ ¼ = 1 x 4/1 = 4

So therefore, g(x) is the image of f(x) after stretched horizontally by scale factor = 4