Question

The function f(x) has been reflected across the x-axis, horizontally compressed by a factor of 1/3, shifted 10 units to the left, and 5 units down. Write an equation in function notation to represent these transformations. Enter your answer as g(x)= a f(1/b x - h) +k

A) g(x) = f(3x + 10) - 5
B) g(x) = f(1/3x + 10) - 5
C) g(x) = f(3x - 10) + 5
D) g(x) = f(1/3x - 10) + 5

Answer 1

The function g(x) that represents the given transformations is g(x) = f(1/3x - 10) - 5.

Step-by-step explanation:

The function g(x) that represents the given transformations is g(x) = f(1/3x - 10) - 5.

To understand the steps involved in the transformation, let's break it down:

1. Reflecting across the x-axis: This is represented by -f(x).
2. Horizontally compressing by a factor of 1/3: This is represented by 1/3x.
3. Shifting 10 units to the left: This is represented by -10.
4. Shifting 5 units down: This is represented by -5.

Combining all these transformations, we get g(x) = f(1/3x - 10) - 5.