Free Printable WorksheetMathAlgebra IIMath CurriculumF-BF.4a

ALG2.86 Determining When a Function Is One to One Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.86 Determining When a Function Is One to One. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.86 Determining When a Function Is One-to-One - Select the correct use of the horizontal line test and reasoning to determine whether a function is one-to-one and how to restrict its domain if needed. Associated source-listed standards: CCSS F-BF.4a; CA CCSSM F-BF.4a; MA 2017 F-BF.4a; NY NGLS F-BF.4a; TX TEKS Algebra II: §111.40.

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 II

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 ALG2.86 Determining When a Function Is One to One skill assessments:

Problem 1Difficulty: Mastery
If q is one-to-one and q(x2 - 4) = q(5), what are the possible values of x?
A3 only
B-3 only
C-3 or 3
Dno real solutions
Solution & Explanation:Since q is one-to-one, the inputs must be equal: x2 - 4 = 5. That gives x2 = 9, so x = -3 or x = 3.
Problem 2Difficulty: Mastery
A quadratic function is restricted to one branch and becomes one-to-one. Which statement must then be true about its inverse?
AThe inverse can never be one-to-one.
BThe inverse is also a function.
CThe inverse has the same domain as the original function.
DThe inverse must be a polynomial.
Solution & Explanation:Restricting to one branch makes the quadratic one-to-one. A one-to-one function has an inverse relation that is a function.
Problem 3Difficulty: Mastery
Which domain restriction makes g(x) = (x + 2)2 - 7 one-to-one and makes g^(-1)(9) the smaller x-value?
Ax >= 2
Ball real numbers
Cx >= -2
Dx <= -2
Solution & Explanation:Solving (x + 2)2 - 7 = 9 gives x = 2 or x = -6. The smaller x-value lies on the left branch, so the correct restriction is x <= -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 II Math students. It aligns with educational standard F-BF.4a (Select the correct use of the horizontal line test and reasoning to determine whether a function is one-to-one and how to restrict its domain if needed. Associated source-listed standards: CCSS F-BF.4a; CA CCSSM F-BF.4a; MA 2017 F-BF.4a; NY NGLS F-BF.4a; TX TEKS Algebra II: §111.40.).

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