This is a collection of practice problems and solutions on the topic of functions from around the web. A few of the problems were written by our tutors but most of the material was created by professors at various universities and colleges for their introductory math courses. The content here takes the form of worksheets, homework, quizzes, and exams, with solutions provided in all cases. We’ve also included some of the best relevant references and videos available online.
We think these questions, solutions, and references make for excellent material for students learning precalculus (in high school or college) or those engaged in self study. Please write to us at info@tutorterrace.com if you have any questions or suggestions. Happy learning!
Basic concept, domain, range, graph, and word problems (applications)
Worksheet 1, Solutions; Worksheet 2, Solutions; Worksheet 3, Solutions; Worksheet 4, Solutions (University of Michigan, DHSP) || Worksheet, Solutions (R Zhao, Berkeley) || Worksheet, Solutions (Prof Buehler, UC Berkeley) || Practice test, Solutions (Prof Vincent, University of Vermont; includes problems on intercepts, asymptotes and holes)
You can read about the function concept, domain, range, composition, inverse and transformations in chapter 1 of this concise opensource textbook by David Lippman and Melonie Rasmussen.
Chapter 1 of this textbook from OpenStax also explains these topics.
This video by Sal Khan has a clear discussion of the basic concept of a function and it’s domain/range.
This video by the The Organic Chemistry Tutor explains how to compute the inverse of a function.
This video by The Organic Chemistry Tutor discusses function composition.
UC Irvine has created an entire series of free videos on functions and graphs as part of their UCI Open initivative.
Function composition and Inverse
Tutor Terrace worksheet and solutions || Worksheet 1, Solutions; Worksheet 2, Solutions; Worksheet 3, Solutions; Worksheet 4, Solutions; Worksheet 5, Solutions (University of Michigan, DHSP) || Practice test, Solutions (Prof Lenz, UCSD) || Worksheet, Solutions (R Fernando, UC Berkeley) || Homework (see Page 2), Solutions (Dr. Pedram, Harvard)
Holes, Zeroes, Intercepts and Asymptotes
Quiz 1, Solutions; Quiz 2, Solutions; Quiz 3, Solutions (Prof Lenz, UCSD) || Worksheet 1, Solutions; Worksheet 2, Solutions (University of Michigan)
This video by Sal Khan discusses asymptotes of rational functions.
This video by The Organic Chemistry Tutor discusses holes in a domain as well as asymptotes.
Periodic functions
Worksheet 1, Solutions; Worksheet 2, Solutions; Worksheet 3, Solutions (University of Michigan) || Tutor Terrace worksheet and solutions
You can read about periodic functions in chapter 6 of this concise opensource textbook by David Lippman and Melonie Rasmussen.
Chapter 6 of this textbook from OpenStax also explains these topics.
This short video from Nerdstudy has a quick introduction to the periodic function concept.
This video by Prof Sam Gralla discusses whether the sum of periodic functions is itself periodic.
This video by blackpenredpen uses examples to discuss some common terminology associated with circular/trigonometric functions.
This video by Dr. Trefor Bazett discusses periodic functions and introduces the idea of a Fourier Series (writing a periodic function as a sum of sin and cosine functions).
