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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: Moderate

Input and Output Tables: Difficult

Evaluate Absolute Value Expression

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

Evaluate Absolute Value: Moderate

Evaluate Absolute Value: Difficult

Solving Absolute Value Equation

Existence of the Solution:

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

Easy:

Moderate:

Difficult:

Type 1: | x | = a

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

Easy:

Moderate:

Type 2: |x + a| = b

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

Easy:

Moderate:

Type 3: a |bx + c| = d

Isolate the absolute value expression and then solve.

Easy:

Moderate:

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

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

Easy:

Moderate:

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

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

Easy:

Moderate:

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.

Easy:

Moderate:

Difficult:

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:

Vertical shift + Horizontal shift:

Graphing Functions: Moderate 1

Vertical shift + Horizontal shift + Reflection:

Graphing Functions: Difficult 1

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