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Absolute Value Equation and Function Worksheets

The worksheets cover solving absolute value expression with input and output table, evaluating expression, solving absolute value equation and graphing function.

Solving Absolute Value Expression

Input and Output Tables

Using the input values and the rule, find out the output values of the absolute value function.

Input and Output Tables: Easy

Input and Output Tables: Medium

Input and Output Tables: Hard

Evaluate Absolute Value Expression

Find the value of each absolute value expression for the particular value of x.

Evaluate Absolute Value: Easy

Evaluate Absolute Value: Medium

Evaluate Absolute Value: Hard

Solving Absolute Value Equation

Existence of the Solution:

The questions may have solutions or no solution. Choose the correct choice.

Easy Level: Sheet 1 | Sheet 2

Medium Level: Sheet 1 | Sheet 2

Hard Level: Sheet 1 | Sheet 2

Type 1: | x | = a

Solve the absolute value equation and find the solutions. The question either has two solutions or no solution.

Easy Sheet 1 | Easy Sheet 2

Medium Sheet 1 | Medium Sheet 2

Type 2: |x + a| = b

Set x + a = b and x + a = -b, and solve the absolute value equations.

Easy Sheet 1 | Easy Sheet 2

Medium Sheet 1 | Medium Sheet 2

Type 3: a |bx + c| = d

Isolate the absolute value expression and then solve.

Easy Sheet 1 | Easy Sheet 2

Medium Sheet 1 | Medium Sheet 2

Type 4: a |bx + c| + d = e

Isolate the absolute value expression from the constant term and solve for x.

Easy Sheet 1 | Easy Sheet 2

Medium Sheet 1 | Medium Sheet 2

Type 5: |ax + b| = |cx + d|

Find the break points, set the interval, solve for x and check for extraneous solution.

Easy Sheet 1 | Easy Sheet 2

Medium Sheet 1 | Medium Sheet 2

Graphing Absolute Value Function

Identify the Absolute Value Function

The graph of the absolute value functions includes vertical shift, horizontal shift and reflection. Identify the absolute value function in each graph.

Identifying Function: Easy 1

Identifying Function: Easy 2

Identifying Function: Medium 1

Identifying Function: Medium 2

Identifying Function: Hard 1

Identifying Function: Hard 2

Graphing Absolute Value Function

Each question contains a function and the grid. Identify the transformations involved in the function and then graph.

Vertical / Horizontal shift:

Graphing Functions: Easy 1

Graphing Functions: Easy 2

Vertical shift + Horizontal shift:

Graphing Functions: Medium 1

Graphing Functions: Medium 2

Vertical shift + Horizontal shift + Reflection:

Graphing Functions: Hard 1

Graphing Functions: Hard 2

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