Created by Catherine Rayno
13 questions
9th - 12th Grade
Math
Updated Oct 2026
Graphing Absolute Value Inequalities is a free printable worksheet for Grade 9–12 mathematics students studying Algebra II. Its 13 multiple-choice questions ask students to identify transformations in absolute value functions, including horizontal and vertical shifts, reflections, and stretches; match equations to graphs; determine equations from graphs; identify vertices; and interpret inequality graphs. Students also practise deciding whether an inequality boundary should be solid or dotted and whether the solution region should be shaded above or below the graph. The varied visual and symbolic questions help students connect an absolute value equation or inequality to its vertex, direction, scale factor, boundary, and shaded region. Use the worksheet for guided practice, independent review, or a quick check of graph interpretation. It is available as a free printable worksheet with a complete answer key.
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WorksheetsAnswer Keyf(x) = 5|x - 4| - 1
Reflect over x-axis, Up 4
C
No
y ≤ |x-4| -1
y > -2|x| + 4
y ≥ -2|x-1| + 1
Solid
Below
(3,1)
This worksheet contains 13 multiple-choice questions on interpreting absolute value functions and inequalities from equations and graphs. Students identify shifts, reflections, and vertical stretches; match equations with graphs; determine equations from graphs; find vertices; and choose the correct boundary style and shading direction. These tasks build the skill of connecting an absolute value expression to the key features shown in its graph.
Introduce the worksheet by reviewing how the form y = a|x − h| + k reveals the vertex, transformations, and opening direction. Model one equation-to-graph and one graph-to-equation example, then have students explain why a boundary is solid or dotted and why the region is shaded above or below. Use the multiple-choice items for guided discussion before assigning the remaining questions independently.
Watch for students reversing the horizontal shift, reading the vertex incorrectly, or treating a negative coefficient as a vertical shift instead of a reflection. In the inequality items, students may confuse solid and dotted boundaries or shade the wrong side of the graph. Students may also select a graph with the correct general shape but the wrong vertex or vertical stretch, so ask them to verify each feature against the equation.
The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 13 multiple-choice questions. For printable submissions, you can scan student work with the Wayground for Teachers app to support grading and review. The printable format also gives schools an option for reducing screen time.
Use the worksheet’s Advanced Settings to adjust font spacing and font size so the equations, graph choices, and inequality prompts are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when appropriate. These options apply to the worksheet file while preserving its multiple-choice format.
Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.
