Free Printable WorksheetMathPre-CalculusMath CurriculumSMP 1,2,4,5,8

Pre CAL.181 Concept of Limit from Tables and Graphs Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.181 Concept of Limit from Tables and Graphs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.181 Concept of Limit from Tables and Graphs - Primary standard selected for prompt fields in this prompt cell: SMP 1,2,4,5,8. Skill statement in this prompt cell: Given a table or graph near a point, determine the limit value (if it exists) and select the correct statement about the behavior as x approaches the point. 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.181 Concept of Limit from Tables and Graphs skill assessments:

Problem 1Difficulty: Mastery

A final table near x = 12 gives x-values: 11.8, 11.98, 12.02, 12.2 and H(x)-values: -3.4, -3.04, -2.96, -2.6. Which statement is the best conclusion about lim_{x->12} H(x)?

AThe limit is -3 because H(x) approaches -3 from both sides.

BThe limit is 12 because x approaches 12.

CThe limit does not exist because the outputs are not exactly equal.

DThe limit is -2.6 because the rightmost output is closest to the final x-value listed.

Solution & Explanation:The outputs near x = 12 approach -3 from the left and the right, so the limit is -3.

Problem 2Difficulty: Mastery

Use the graph shown near x = -5. The curve has small holes away from x = -5, but the branch approaching x = -5 from both sides tends to y = 2. Which statement is best?

AThe limit at x = -5 is 2 because the behavior near -5 approaches y = 2.

BThe limit does not exist because there are holes somewhere on the graph.

CThe limit is -5 because x approaches -5.

DThe limit is the y-value of the nearest hole away from x = -5.

Solution & Explanation:Limits are local to the target input. Other holes away from x = -5 do not matter if values near -5 approach y = 2.

Problem 3Difficulty: Mastery

The graph shown approaches y = 8 from below on the left and from above on the right as x approaches 6. Which statement is true?

AThe limit is 8 because both sides approach the same y-value.

BThe limit does not exist because one side is below 8 and the other is above 8.

CThe limit is 6 because x approaches 6.

DThe limit is 0 because the approaches are opposite.

Solution & Explanation:Approaching from below and above can still lead to the same limit. Both sides move toward y = 8.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

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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 SMP 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 table or graph near a point, determine the limit value (if it exists) and select the correct statement about the behavior as x approaches the point. 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.).