Question

Write the equation that results if the parent absolute value is shifted right 15 units, down 3 units, and reflected vertically.

a) f(x) = |x - 15| - 3
b) f(x) = -|x - 15| - 3
c) f(x) = |x + 15| - 3
d) f(x) = |x - 15| + 3

Answer 1

The equation that results if the parent absolute value is shifted right 15 units, down 3 units, and reflected vertically is f(x) = |x - 15| - 3.

Step-by-step explanation:

The equation that results if the parent absolute value is shifted right 15 units, down 3 units, and reflected vertically is f(x) = |x - 15| - 3.

To shift the absolute value function right 15 units, we subtract 15 from the x inside the absolute value. To shift it down 3 units, we subtract 3 from the entire expression. And to reflect it vertically, we just change the sign of the entire expression.

Let's break it down step by step:
1. Start with the parent absolute value function: f(x) = |x|
2. Shift right 15 units: f(x) = |x - 15|
3. Shift down 3 units: f(x) = |x - 15| - 3
4. Reflect vertically: f(x) = -(|x - 15| - 3)
Simplifying the expression: f(x) = -|x - 15| + 3