Free Printable WorksheetMathPre-CalculusMath CurriculumHSF-IF.1-6,9

Pre CAL.18 Identify Increasing, Decreasing, Positive, and Negative Intervals Worksheet

Download our free printable Pre-Calculus Math worksheet on Pre CAL.18 Identify Increasing, Decreasing, Positive, and Negative Intervals. 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

Download PDFDownload DOCX
Prefer interactive practice with instant grading and explanations?Practice Identify Increasing, Decreasing, Positive, and Negative Intervals Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.18 Identify Increasing, Decreasing, Positive, and Negative Intervals. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.18 Identify Increasing, Decreasing, Positive, and Negative Intervals - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.1-6,9. Skill statement in this prompt cell: Given a graph, determine the interval(s) where the function is increasing, decreasing, positive, or negative and select the correct interval notation. Associated standards listed with this skill in this prompt cell: CCSS HSF-IF.1-6,9; CCSS HSF-BF.1-4; CCSS HSA-CED.1-4; SMP 1,2,4,5,7; AP Precalculus CED Units 1-3; TX §111.42(c)(2)(A-L); FL MA.912.F.1.4, MA.912.F.1.7, MA.912.F.3.3-3.9, MA.912.AR.9.10; VA MA.CF.1, MA.FR.1. 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.18 Identify Increasing, Decreasing, Positive, and Negative Intervals skill assessments:

Problem 1Difficulty: Mastery
A graph is positive on (-7, -2), (0, 4), and (9, infinity). It is decreasing on (-8, -5), (-1, 2), and (6, 10). Which interval notation represents where f(x) > 0 and f is decreasing?
A(-7, -2) U (0, 4) U (9, infinity)
B(-8, -5) U (-1, 2) U (6, 10)
C(-5, 0) U (4, 9)
D(-7, -5) U (0, 2) U (9, 10)
Solution & Explanation:The graph must be both above the x-axis and falling. The overlaps are (-7,-5), (0,2), and (9,10).
Problem 2Difficulty: Mastery
A graph is positive on (-9, -4), (0, 2), and (6, 10). It is decreasing on (-7, -5), (-1, 1), and (4, 8). Which interval notation represents where f(x) > 0 but f is not decreasing?
A(-9, -4) U (0, 2) U (6, 10)
B(-7, -5) U (-1, 1) U (4, 8)
C(-9, -7) U (-5, -4) U (1, 2) U (8, 10)
D(-7, -5) U (0, 1) U (6, 8)
Solution & Explanation:Start with the positive intervals and remove the parts where the graph is decreasing. That leaves (-9,-7), (-5,-4), (1,2), and (8,10).
Problem 3Difficulty: Mastery
A graph is negative on (-infinity, -9), (-5, -2), (1, 4), and (4, 8), with a removable hole at x = 4. It is increasing on (-10, -7), (-4, 0), and (3, 6). Which interval notation represents where f(x) < 0 and f is increasing?
A(-infinity, -9) U (-5, -2) U (1, 8)
B(-10, -9) U (-4, -2) U (3, 4) U (4, 6)
C(-10, -7) U (-4, 0) U (3, 6)
D(-9, -5) U (-2, 1) U (6, 8)
Solution & Explanation:The target intervals are the overlaps of negative and increasing regions. The hole at x = 4 splits the last overlap into (3,4) and (4,6).

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.18 Identify Increasing, Decreasing, Positive, and Negative Intervals 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.18 Identify Increasing, Decreasing, Positive, and Negative Intervals 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.18 Identify Increasing, Decreasing, Positive, and Negative Intervals online with instant feedback?

Yes! In addition to this printable worksheet, students can practice Pre CAL.18 Identify Increasing, Decreasing, Positive, and Negative Intervals 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 HSF-IF.1-6,9 (Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.1-6,9. Skill statement in this prompt cell: Given a graph, determine the interval(s) where the function is increasing, decreasing, positive, or negative and select the correct interval notation. Associated standards listed with this skill in this prompt cell: CCSS HSF-IF.1-6,9; CCSS HSF-BF.1-4; CCSS HSA-CED.1-4; SMP 1,2,4,5,7; AP Precalculus CED Units 1-3; TX §111.42(c)(2)(A-L); FL MA.912.F.1.4, MA.912.F.1.7, MA.912.F.3.3-3.9, MA.912.AR.9.10; VA MA.CF.1, MA.FR.1. 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

More Pre-Calculus Worksheets

Pre CAL.1 Function Notation and Evaluating Functions
Pre CAL.10 Inverse Functions and One to One Relationships
Pre CAL.100 Solve Triangles Including the Ambiguous Case
Pre CAL.101 Find the Area of a Triangle Using Trigonometry
Browse all Pre-Calculus Worksheets

Interactive Online Skills

Pre-CAL.1Function Notation and Evaluating Functions
Pre-CAL.2Domain, Range, and Function Types
Pre-CAL.3Multiple Representations of Functions
Pre-CAL.4Interpreting Key Features of Functions in Context
Browse all Pre-Calculus Interactive Practice