Question

Let f(x)=3ˣ.

Which function represents a transformation of f(x) by a vertical stretch with factor 6?
a. g(x)=1/6 ⋅ 3ˣ
b. g(x)=3ˣ/6x
c. g(x)=3⁶x
d. g(x)=6 ⋅ 3ˣ

Answer 1

To represent a vertical stretch with factor 6 of the function f(x) = 3^x, we must multiply the output by 6. The correct function for this transformation is g(x) = 6 · 3^x. Options (a), (b), and (c) do not accurately represent a vertical stretch of factor 6.

Step-by-step explanation:

The student has asked which function represents a transformation of the function f(x) = 3x by a vertical stretch with factor 6. A vertical stretch of a function by a factor of 6 means that the output of the function will be multiplied by 6. Therefore, the transformed function g(x) will represent the original function's output multiplied by 6.

The correct answer is:

• g(x) = 6 · 3x

Options (a), (b), and (c) do not represent a vertical stretch of factor 6. Specifically, option (a) represents a vertical compression by a factor of 6, option (b) is an incorrect transformation not related to a vertical stretch, and option (c) changes the exponent instead of stretching the function.