Question

The parent function f(x) = |x| is reflected across the x-axis, translated three units left, and two units down. Which is the transformed function?

A. g(x) = |x| - 3 - 2
B. g(x) = |x + 3| - 2
C. g(x) = |x| + 3 + 2
D. g(x) = |x - 3| + 2

Answer 1

The transformed function after the given transformations is g(x) = |x + 3| - 2, which corresponds to option B.

Step-by-step explanation:

To determine the transformed function of f(x) = |x| after it has been reflected across the x-axis, translated three units to the left, and translated two units down, we apply a series of transformations step by step.

Firstly, reflecting a function across the x-axis will multiply the function by -1. Thus, the reflection of f(x) across the x-axis is -|x|.

Secondly, translating a function to the left by 3 units means replacing x with (x + 3). Hence, our function is now -|x + 3|.

Finally, translating the function down by 2 units means subtracting 2 from the function, so the entire transformed function becomes g(x) = -|x + 3| - 2. But the options provided in the question do not directly match this. Noticing that reflecting the absolute function across the x-axis is the same as putting a minus before the absolute value, we can add 2 to both sides to find the correct option, which leads to g(x) = |x + 3| - 2, matching option B.