Question

Given the function f(x) = 3x⁵, perform a vertical shrink by a factor of 1/3. What is the transformed function?

a) g(x) = (1/3)x⁵
b) g(x) = 3x⁵
c) g(x) = x⁵/3
d) g(x) = 3x²

Answer 1

A vertical shrink by a factor of 1/3 of the function f(x) = 3x⁵ results in the transformed function f(x) = x⁵. The shrinking process involves multiplying the original function's coefficient by the shrink factor, which changes the coefficient from 3 to 1.

Step-by-step explanation:

The student is asking about a transformation that involves a vertical shrink of the function f(x) = 3x⁵ by a factor of 1/3. When we apply a vertical shrink to a function, we multiply the function's output by the shrink factor. In this case, the original function needs to be multiplied by 1/3.

To demonstrate this, let's take the function f(x) = 3x⁵ and apply the vertical shrink:

• The original coefficient of the function is 3.
• We then multiply this coefficient by the shrink factor, which is 1/3.
• So, 3 × (1/3) equals 1, which becomes the new coefficient of the transformed function.
• Hence, the transformed function after applying a vertical shrink by a factor of 1/3 to f(x) = 3x⁵ will be f(x) = x⁵.

This new function f(x) = x⁵ represents a function that has been shrunk vertically by 1/3, meaning the height of its graph at any given x-value will be 1/3 of the height of the original function's graph at the same x-value.