Question

9/41
which equation represents an absolute value function shifted down 3 units?
y = |x| + 3
y = |x - 3|
y = |x + 3|
y = |x| - 3

Explanation:

Step1: Recall vertical shift rule

For a function \( y = f(x) \), a vertical shift down by \( k \) units is \( y = f(x)-k \).

Step2: Apply to absolute value function

The parent absolute value function is \( y = |x| \). Shifting down 3 units means subtracting 3 from the function. So the equation is \( y = |x| - 3 \).

Answer:

D. \( y = |x| - 3 \) (assuming the options are labeled A, B, C, D in order as shown: A. \( y = |x| + 3 \), B. \( y = |x - 3| \), C. \( y = |x + 3| \), D. \( y = |x| - 3 \))