Free Printable WorksheetMathPre-CalculusMath CurriculumHSF-TF.1-9(+)

Pre CAL.93 Determine Domain and Range of Trigonometric Functions from 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.93 Determine Domain and Range of Trigonometric Functions from Graphs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.93 Determine Domain and Range of Trigonometric Functions from Graphs - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-TF.1-9(+). Skill statement in this prompt cell: Given a trigonometric function graph, identify its domain and range and select any excluded values caused by asymptotes or restrictions. Associated standards listed with this skill in this prompt cell: CCSS HSF-TF.1-9(+); CCSS HSF-IF.7e; CCSS HSG-SRT.C.6-8; SMP 1,2,3,5,7,8; AP Precalculus CED Unit 3; TX §111.42(c)(4)(A-D), (c)(5)(I); FL MA.912.T.1.3-1.8, MA.912.T.2.1-2.5, MA.912.T.3.1-3.3, MA.912.T.4.1-4.7; VA T.CT.1-2, T.GT.1-2, T.IE.1-3. 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.93 Determine Domain and Range of Trigonometric Functions from Graphs skill assessments:

Problem 1Difficulty: Mastery
The graph shows y = -3csc(x) + 1 over all allowed x-values. Which domain and range match the graph?
ADomain: x!= k*pi; Range: (-infinity, -2] U [4, infinity)
BDomain: x!= pi/2 + k*pi; Range: [-2, 4]
CDomain: all real numbers; Range: (-infinity, -2] U [4, infinity)
DDomain: x!= k*pi; Range: [-2, 4]
Solution & Explanation:Cosecant is undefined at x = k*pi. Applying y = -3csc(x) + 1 to csc values of 1 and -1 gives branch vertices -2 and 4, so the range is y <= -2 or y >= 4.
Problem 2Difficulty: Mastery
A secant graph has vertical asymptotes at x = pi/2 + k*pi. The upper branch vertices are at y = 5 and the lower branch vertices are at y = 1. Which range is correct?
A[1, 5]
B(-infinity, 1] U [5, infinity)
C(-infinity, 5] U [1, infinity)
Dall real numbers except 1 and 5
Solution & Explanation:Secant branches do not fill the interval between the lower and upper vertices. The range is y <= 1 or y >= 5.
Problem 3Difficulty: Mastery
The graph shows y = csc(x) on -5pi/6 <= x <= 7pi/6, with asymptotes at x = 0 and x = pi. What are the displayed domain and range?
ADomain: [-5pi/6, 0) U (0, pi) U (pi, 7pi/6]; Range: (-infinity, -1] U [1, infinity)
BDomain: [-5pi/6, 7pi/6]; Range: [-1, 1]
CDomain: (-5pi/6, 0) U (0, 7pi/6); Range: all real numbers
DDomain: x!= pi/2 + k*pi; Range: (-infinity, -1] U [1, infinity)
Solution & Explanation:Cosecant is undefined at x = 0 and x = pi in the display. The included branches reach y <= -1 and y >= 1, with no values between -1 and 1.

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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 Pre-Calculus Math students. It aligns with educational standard HSF-TF.1-9(+) (Primary standard selected for prompt fields in this prompt cell: CCSS HSF-TF.1-9(+). Skill statement in this prompt cell: Given a trigonometric function graph, identify its domain and range and select any excluded values caused by asymptotes or restrictions. Associated standards listed with this skill in this prompt cell: CCSS HSF-TF.1-9(+); CCSS HSF-IF.7e; CCSS HSG-SRT.C.6-8; SMP 1,2,3,5,7,8; AP Precalculus CED Unit 3; TX §111.42(c)(4)(A-D), (c)(5)(I); FL MA.912.T.1.3-1.8, MA.912.T.2.1-2.5, MA.912.T.3.1-3.3, MA.912.T.4.1-4.7; VA T.CT.1-2, T.GT.1-2, T.IE.1-3. Use this prompt-provided wording as the supporting standard description for this workflow.).

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