Absolute Value Functions Practice

Absolute Value Functions

Practice matching, transformations, and equation writing.

Part 1: Multiple Choice

1. The graph of f(x) = |x - 5| is a transformation of f(x) = |x|. What type of transformation is this?

A. Horizontal shift 5 units to the right B. Horizontal shift 5 units to the left C. Vertical shift 5 units up D. Reflection over the y-axis

2. The graph of f(x) = 3|x| is a transformation of f(x) = |x|. What type of transformation is this?

A. Vertical compression by a factor of 3 B. Vertical stretch by a factor of 3 C. Horizontal stretch by a factor of 3 D. Horizontal compression by a factor of 3

Part 2: Fill in the Blank

Write the equation of the absolute value function based on the transformations described. Enter numbers only.

Shift 3 units left and 2 units down:

f(x) = |x + | -

Vertical stretch by a factor of 2 and shift 5 units up:

f(x) = |x| + 5

Part 3: Multiple Selection (Challenge Problem)

Select ALL transformations applied to the graph of f(x) = |x| to obtain:

f(x) = -3|x - 2| + 4

Part 4: Choice Matrix

Identify the single primary transformation for each function below compared to f(x) = |x|. Select one per row.

Function	Shift Down 2	Shift Left 2	Reflect x-axis

Part 5: Match the Transformations

Tap a description below to select it, then tap an empty slot next to the matching equation to place it.