Question

What transformations are applied to the graph of the function f(x)=10^x to produce the function g(x)=3(10)^x-2

A.) a vertical dilation by a factor of 3 and a horizontal shift to the right 2 units

B.) a vertical dilation by a factor of 1/3 and a horizontal shift to the right 2 units

C.) a vertical dilation by a factor of 1/3 and a vertical shift down 2 units

D.) a vertical dilation by a factor of 3 and a vertical shift down 2 units

Answer 1

• D) A vertical dilation by a factor of 3 and a vertical shift down 2 units

Explanation:

Given

• f(x)=10^x
• g(x)=3(10)^x - 2

We see that:

• g(x) = 3f(x) - 2

This is a vertical stretch by a factor of 3 and translation down 2 units

Correct choice is D