Question

Let f(x)=3x. which function represents a transformation of f(x) by a vertical stretch with factor 6?

Option 1: g(x)=6⋅3x
Option 2: g(x)=36x
Option 3: g(x)=316x
Option 4: g(x)=16⋅3x

Answer 1

The function that represents a vertical stretch of f(x) = 3x with factor 6 is g(x) = 6· 3x, which corresponds to Option 1.

Step-by-step explanation:

To determine which function represents a transformation of the function f(x) = 3x by a vertical stretch with a factor of 6, we need to multiply the original function by 6. Therefore, the function that represents a vertical stretch with factor 6 is: g(x) = 6 · 3x .This is because a vertical stretch by a factor of k multiplies the output value of the function by k. Since the original function is f(x) = 3x, a vertical stretch by a factor of 6 would make it g(x) = 6 · 3x. Option 1 is the correct choice: g(x)=6· 3x.The function f(x) = 3x represents a linear function with a positive slope. To vertically stretch this function by a factor of 6, we need to multiply the function by 6. Therefore, the function g(x) = 6 ⋅ 3x represents a transformation of f(x) by a vertical stretch with factor 6.