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ALG1.109 Piecewise Defined Functions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.109 Piecewise Defined Functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.109 Piecewise-Defined Functions - Select the correct value of and graph piecewise-defined functions, including step functions; Select the statement that correctly interprets open and closed endpoints and domain restrictions from the definition. (CCSS: F-IF.7b; TEKS: §111.39(c)(3)(C) (key features), (8) (district scope varies); VA SOL: A.F.2 (comparisons across parent functions); FL B.E.S.T.: MA.912.AR.4.3 (absolute value graphs), MA.912.F.1.1 (parent functions); NY-NGLS: AI-F.IF.7b; CA CCSSM: F-IF.7b; MA 2017: HS.F-IF.7b; DoDEA CCRSM; NAEP: Algebra—graphs; NCTM P2A: Practices 2, 7.)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra I

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG1.109 Piecewise Defined Functions skill assessments:

Problem 1Difficulty: Mastery
Let f(x) = 2x - 4 for x < 3; f(x) = a for x >= 3. The graph has a closed point at (3, 6) on the second piece. Which value of a and first-piece endpoint are correct?
Aa = 6, and the first piece has an open circle at (3, 2)
Ba = 2, and the first piece has a closed circle at (3, 2)
Ca = 6, and the first piece has a closed circle at (3, 6)
Da = 2, and the first piece has an open circle at (3, 6)
Solution & Explanation:The closed point on the second piece gives f(3) = a = 6. The first rule would give 2(3) - 4 = 2, but x = 3 is not included in x < 3, so that endpoint is open.
Problem 2Difficulty: Mastery
Use the graph shown with boundaries at x = -1 and x = 3. Which statement is true?
AThe domain is x >= -4, f(-1) = 2, f(3) = 2, and there is a jump at x = -1 but not at x = 3.
BThe domain is all real numbers, f(-1) = 0, and f(3) is undefined.
CThe domain is -4 < x < 3, and both endpoints at x = -1 are open.
DThe function has jumps at both x = -1 and x = 3 because all boundaries cause jumps.
Solution & Explanation:The graph starts at x = -4 and continues right. The closed points give f(-1) = 2 and f(3) = 2. The y-value changes at x = -1 but matches at x = 3.
Problem 3Difficulty: Mastery
A piecewise graph for y = ax + 1 on x < 2 has an open circle at (2, 5). What is a?
A1
B2
C3
D4
Solution & Explanation:The open endpoint still lies on the line y = ax + 1. Substitute (2, 5): 5 = 2a + 1, so 2a = 4 and a = 2.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra I Math students. It aligns with educational standard F-IF.7b (Primary standard selected for prompt fields in this prompt cell: CCSS F-IF.7b. Skill statement in this prompt cell: Select the correct value of and graph piecewise-defined functions, including step functions; Select the statement that correctly interprets open and closed endpoints and domain restrictions from the definition. Associated standards listed with this skill in the curriculum source: CCSS: F-IF.7b; TEKS: §111.39(c)(3)(C) (key features), (8) (district scope varies); VA SOL: A.F.2 (comparisons across parent functions); FL B.E.S.T.: MA.912.AR.4.3 (absolute value graphs), MA.912.F.1.1 (parent functions); NY-NGLS: AI-F.IF.7b; CA CCSSM: F-IF.7b; MA 2017: HS.F-IF.7b; DoDEA CCRSM; NAEP: Algebra—graphs; NCTM P2A: Practices 2, 7. Use this prompt-provided wording as the supporting standard description for this workflow.).

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