Free Printable WorksheetMathPre-CalculusMath Curriculum1,2,4,5,8

Pre CAL.182 One Sided and Two Sided Limits and Discontinuities Worksheet

Download our free printable Pre-Calculus Math worksheet on Pre CAL.182 One Sided and Two Sided Limits and Discontinuities. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

Choose your preferred download format:

100% Free • No registration or login required • Instant file access

Prefer interactive practice with instant grading and explanations?Practice One-Sided and Two-Sided Limits and Discontinuities Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.182 One Sided and Two Sided Limits and Discontinuities. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.182 One-Sided and Two-Sided Limits and Discontinuities - Primary standard selected for prompt fields in this prompt cell: SMP 1,2,4,5,8. Skill statement in this prompt cell: Given a graph or piecewise definition, determine left-hand and right-hand limits and select whether the two-sided limit exists. Associated standards listed with this skill in this prompt cell: SMP 1,2,4,5,8; VA MA.CF.2-3; NCTM CCHS. Use this prompt-provided wording as the supporting standard description for this workflow.

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

Pre-Calculus

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 Pre CAL.182 One Sided and Two Sided Limits and Discontinuities skill assessments:

Problem 1Difficulty: Mastery
For f(x) = x + 2 when x < -1, f(x) = 1 when -1 < x < 2, and f(x) = x - 3 when x > 2, which x-value has a two-sided limit that does not exist?
Ax = -1 only
Bx = 2 only
Cboth x = -1 and x = 2
Dneither x = -1 nor x = 2
Solution & Explanation:At x = -1, the left and right limits both equal 1. At x = 2, the left-hand limit is 1 but the right-hand limit is -1, so the two-sided limit does not exist.
Problem 2Difficulty: Mastery
A jump discontinuity can still have a two-sided limit if the graph has a filled dot on one side of the jump.
ATrue
BFalse
Solution & Explanation:A jump discontinuity means the one-sided limits are different. A filled dot affects f(a), not the matching of the one-sided limits.
Problem 3Difficulty: Mastery
If the two-sided limit exists at x = a, then the left-hand and right-hand limits must be equal, even if f(a) is undefined.
ATrue
BFalse
Solution & Explanation:The equality of the two one-sided limits is what determines the two-sided limit. f(a) may be undefined.

Want more practice questions with step-by-step guidance?

Practice All Questions Online

Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this Pre CAL.182 One Sided and Two Sided Limits and Discontinuities worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this Pre CAL.182 One Sided and Two Sided Limits and Discontinuities worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice Pre CAL.182 One Sided and Two Sided Limits and Discontinuities online with instant feedback?

Yes! In addition to this printable worksheet, students can practice Pre CAL.182 One Sided and Two Sided Limits and Discontinuities interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard 1,2,4,5,8 (Primary standard selected for prompt fields in this prompt cell: SMP 1,2,4,5,8. Skill statement in this prompt cell: Given a graph or piecewise definition, determine left-hand and right-hand limits and select whether the two-sided limit exists. Associated standards listed with this skill in this prompt cell: SMP 1,2,4,5,8; VA MA.CF.2-3; NCTM CCHS. Use this prompt-provided wording as the supporting standard description for this workflow.).

Related Pre-Calculus Math Resources

Continue learning with complementary skill worksheets and online practice