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Section Exercises are organized by question type, and generally appear in the following order:

  • Verbal questions assess conceptual understanding of key terms and concepts.
  • Algebraic problems require students to apply algebraic manipulations demonstrated in the section.
  • Graphical problems assess students’ ability to interpret or produce a graph.
  • Numeric problems require the student perform calculations or computations.
  • Technology problems encourage exploration through use of a graphing utility, either to visualize or verify algebraic results or to solve problems via an alternative to the methods demonstrated in the section.
  • Extensions pose problems more challenging than the Examples demonstrated in the section. They require students to synthesize multiple learning objectives or apply critical thinking to solve complex problems.
  • Real-World Applications present realistic problem scenarios from fields such as physics, geology, biology, finance, and the social sciences.

Chapter review features

Each chapter concludes with a review of the most important takeaways, as well as additional practice problems that students can use to prepare for exams.

  • Key Terms provides a formal definition for each bold-faced term in the chapter.
  • Key Equations presents a compilation of formulas, theorems, and standard-form equations.
  • Key Concepts summarizes the most important ideas introduced in each section, linking back to the relevant Example(s) in case students need to review.
  • Chapter Review Exercises include 40-80 practice problems that recall the most important concepts from each section.
  • Practice Test includes 25-50 problems assessing the most important learning objectives from the chapter. Note that the practice test is not organized by section, and may be more heavily weighted toward cumulative objectives as opposed to the foundational objectives covered in the opening sections.
  • Answer Key includes the answers to all Try It exercises and every other exercise from the Section Exercises, Chapter Review Exercises, and Practice Test.

Ancillaries

OpenStax projects offer an array of ancillaries for students and instructors. Currently the following resources are available.

  • Instructor’s Solutions Manual
  • Student’s Solutions Manual
  • PowerPoint Slides

Please visit http://openstaxcollege.org to view an up-to-date list of the Learning Resources for this title and to find information on accessing these resources.

Online homework

WebAssign

WebAssign is an independent online homework and assessment solution first launched at North Carolina State University in 1997. Today, WebAssign is an employee-owned benefit corporation and participates in the education of over a million students each year. WebAssign empowers faculty to deliver fully customizable assignments and high quality content to their students in an interactive online environment. WebAssign supports Precalculus with hundreds of problems covering every concept in the course, each containing algorithmically-generated values and links directly to the eBook providing a completely integrated online learning experience.

Learningpod is the best place to find high-quality practice and homework questions. Through our partnership with OpenStax we offer easy-to-use assignment and reporting tools for professors and a beautiful practice experience for students. You can find questions directly from this textbook on Learningpod.com or through the OpenStax mobile app. Look for our links at the end of each chapter!
Practice questions on the Learningpod website: www.learningpod.com
Download the OpenStax Companion Workbooks app (iOS): http://bit.ly/openstaxworkbooks

About our team

Lead author, senior content expert

Jay Abramson has been teaching Precalculus for 33 years, the last 14 at Arizona State University, where he is a principal lecturer in the School of Mathematics and Statistics. His accomplishments at ASU include co-developing the university’s first hybrid and online math courses as well as an extensive library of video lectures and tutorials. In addition, he has served as a contributing author for two of Pearson Education’s math programs, NovaNet Precalculus and Trigonometry. Prior to coming to ASU, Jay taught at Texas State Technical College and Amarillo College. He received Teacher of the Year awards at both institutions.

Contributing authors

  • Valeree Falduto, Palm Beach State College
  • Rachael Gross, Towson University
  • David Lippman, Pierce College
  • Melonie Rasmussen, Pierce College
  • Rick Norwood, East Tennessee State University
  • Nicholas Belloit, Florida State College Jacksonville
  • Jean-Marie Magnier, Springfield Technical Community College
  • Harold Whipple
  • Christina Fernandez

Faculty reviewers and consultants

  • Nina Alketa, Cecil College
  • Kiran Bhutani, Catholic University of America
  • Brandie Biddy, Cecil College
  • Lisa Blank, Lyme Central School
  • Bryan Blount, Kentucky Wesleyan College
  • Jessica Bolz, The Bryn Mawr School
  • Sheri Boyd, Rollins College
  • Sarah Brewer, Alabama School of Math and Science
  • Charles Buckley, St. Gregory's University
  • Michael Cohen, Hofstra University
  • Kenneth Crane, Texarkana College
  • Rachel Cywinski, Alamo Colleges
  • Nathan Czuba
  • Srabasti Dutta, Ashford University
  • Kristy Erickson, Cecil College
  • Nicole Fernandez, Georgetown University / Kent State University
  • David French, Tidewater Community College
  • Douglas Furman, SUNY Ulster
  • Lance Hemlow, Raritan Valley Community College
  • Erinn Izzo, Nicaragua Christian Academy
  • John Jaffe
  • Jerry Jared, Blue Ridge School
  • Stan Kopec, Mount Wachusett Community College
  • Kathy Kovacs
  • Cynthia Landrigan, Erie Community College
  • Sara Lenhart, Christopher Newport University
  • Wendy Lightheart, Lane Community College
  • Joanne Manville, Bunker Hill Community College
  • Karla McCavit, Albion College
  • Cynthia McGinnis, Northwest Florida State College
  • Lana Neal, University of Texas at Austin
  • Rhonda Porter, Albany State University
  • Steven Purtee, Valencia College
  • William Radulovich, Florida State College Jacksonville
  • Alice Ramos, Bethel College
  • Nick Reynolds, Montgomery Community College
  • Amanda Ross, A. A. Ross Consulting and Research, LLC
  • Erica Rutter, Arizona State University
  • Sutandra Sarkar, Georgia State University
  • Willy Schild, Wentworth Institute of Technology
  • Todd Stephen, Cleveland State University
  • Scott Sykes, University of West Georgia
  • Linda Tansil, Southeast Missouri State University
  • John Thomas, College of Lake County
  • Diane Valade, Piedmont Virginia Community College
  • Allen Wolmer, Atlanta Jewish Academy

Questions & Answers

how did you get 1640
Noor Reply
If auger is pair are the roots of equation x2+5x-3=0
Peter Reply
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
MATTHEW Reply
420
Sharon
from theory: distance [miles] = speed [mph] × time [hours] info #1 speed_Dennis × 1.5 = speed_Wayne × 2 => speed_Wayne = 0.75 × speed_Dennis (i) info #2 speed_Dennis = speed_Wayne + 7 [mph] (ii) use (i) in (ii) => [...] speed_Dennis = 28 mph speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5. Substituting the first equation into the second: W * 2 = (W + 7) * 1.5 W * 2 = W * 1.5 + 7 * 1.5 0.5 * W = 7 * 1.5 W = 7 * 3 or 21 W is 21 D = W + 7 D = 21 + 7 D = 28
Salma
Devon is 32 32​​ years older than his son, Milan. The sum of both their ages is 54 54​. Using the variables d d​ and m m​ to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
Aaron Reply
find product (-6m+6) ( 3m²+4m-3)
SIMRAN Reply
-42m²+60m-18
Salma
what is the solution
bill
how did you arrive at this answer?
bill
-24m+3+3mÁ^2
Susan
i really want to learn
Amira
I only got 42 the rest i don't know how to solve it. Please i need help from anyone to help me improve my solving mathematics please
Amira
Hw did u arrive to this answer.
Aphelele
hi
Bajemah
-6m(3mA²+4m-3)+6(3mA²+4m-3) =-18m²A²-24m²+18m+18mA²+24m-18 Rearrange like items -18m²A²-24m²+42m+18A²-18
Salma
complete the table of valuesfor each given equatio then graph. 1.x+2y=3
Jovelyn Reply
x=3-2y
Salma
y=x+3/2
Salma
Hi
Enock
given that (7x-5):(2+4x)=8:7find the value of x
Nandala
3x-12y=18
Kelvin
please why isn't that the 0is in ten thousand place
Grace Reply
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
Marry Reply
how far
Abubakar
cool u
Enock
state in which quadrant or on which axis each of the following angles given measure. in standard position would lie 89°
Abegail Reply
hello
BenJay
hi
Method
I am eliacin, I need your help in maths
Rood
how can I help
Sir
hmm can we speak here?
Amoon
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
cameron Reply
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
mahnoor Reply
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67. Check: Sales = 3542 Commission 12%=425.04 Pay = 500 + 425.04 = 925.04. 925.04 > 925.00
Munster
difference between rational and irrational numbers
Arundhati Reply
When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?
Jakoiya Reply
how to reduced echelon form
Solomon Reply
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
Zack Reply
d=r×t the equation would be 8/r+24/r+4=3 worked out
Sheirtina
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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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