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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.


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 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
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  • Rhonda Porter, Albany State University
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  • Nick Reynolds, Montgomery Community College
  • Amanda Ross, A. A. Ross Consulting and Research, LLC
  • Erica Rutter, Arizona State University
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  • Todd Stephen, Cleveland State University
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  • 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

I've run into this: x = r*cos(angle1 + angle2) Which expands to: x = r(cos(angle1)*cos(angle2) - sin(angle1)*sin(angle2)) The r value confuses me here, because distributing it makes: (r*cos(angle2))(cos(angle1) - (r*sin(angle2))(sin(angle1)) How does this make sense? Why does the r distribute once
Carlos Reply
How can you tell what type of parent function a graph is ?
Mary Reply
generally by how the graph looks and understanding what the base parent functions look like and perform on a graph
if you have a graphed line, you can have an idea by how the directions of the line turns, i.e. negative, positive, zero
y=x will obviously be a straight line with a zero slope
y=x^2 will have a parabolic line opening to positive infinity on both sides of the y axis vice versa with y=-x^2 you'll have both ends of the parabolic line pointing downward heading to negative infinity on both sides of the y axis
y=x will be a straight line, but it will have a slope of one. Remember, if y=1 then x=1, so for every unit you rise you move over positively one unit. To get a straight line with a slope of 0, set y=1 or any integer.
yes, correction on my end, I meant slope of 1 instead of slope of 0
what is f(x)=
Karim Reply
I don't understand
Typically a function 'f' will take 'x' as input, and produce 'y' as output. As 'f(x)=y'. According to Google, "The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain."
Sorry, I don't know where the "Â"s came from. They shouldn't be there. Just ignore them. :-)
It is the  that should not be there. It doesn't seem to show if encloses in quotation marks. "Â" or 'Â' ... Â
Now it shows, go figure?
what is this?
unknown Reply
i do not understand anything
lol...it gets better
I've been struggling so much through all of this. my final is in four weeks 😭
this book is an excellent resource! have you guys ever looked at the online tutoring? there's one that is called "That Tutor Guy" and he goes over a lot of the concepts
thank you I have heard of him. I should check him out.
is there any question in particular?
I have always struggled with math. I get lost really easy, if you have any advice for that, it would help tremendously.
Sure, are you in high school or college?
Hi, apologies for the delayed response. I'm in college.
how to solve polynomial using a calculator
Ef Reply
So a horizontal compression by factor of 1/2 is the same as a horizontal stretch by a factor of 2, right?
The center is at (3,4) a focus is at (3,-1), and the lenght of the major axis is 26
Rima Reply
The center is at (3,4) a focus is at (3,-1) and the lenght of the major axis is 26 what will be the answer?
I done know
What kind of answer is that😑?
I had just woken up when i got this message
Can you please help me. Tomorrow is the deadline of my assignment then I don't know how to solve that
i have a question.
how do you find the real and complex roots of a polynomial?
@abdul with delta maybe which is b(square)-4ac=result then the 1st root -b-radical delta over 2a and the 2nd root -b+radical delta over 2a. I am not sure if this was your question but check it up
This is the actual question: Find all roots(real and complex) of the polynomial f(x)=6x^3 + x^2 - 4x + 1
@Nare please let me know if you can solve it.
I have a question
hello guys I'm new here? will you happy with me
The average annual population increase of a pack of wolves is 25.
Brittany Reply
how do you find the period of a sine graph
Imani Reply
Period =2π if there is a coefficient (b), just divide the coefficient by 2π to get the new period
if not then how would I find it from a graph
by looking at the graph, find the distance between two consecutive maximum points (the highest points of the wave). so if the top of one wave is at point A (1,2) and the next top of the wave is at point B (6,2), then the period is 5, the difference of the x-coordinates.
you could also do it with two consecutive minimum points or x-intercepts
I will try that thank u
Case of Equilateral Hyperbola
Jhon Reply
f(x)=4x+2, find f(3)
f(3)=4(3)+2 f(3)=14
pre calc teacher: "Plug in Plug in...smell's good" f(x)=14
Explain why log a x is not defined for a < 0
Baptiste Reply
the sum of any two linear polynomial is what
Esther Reply
divide simplify each answer 3/2÷5/4
Momo Reply
divide simplify each answer 25/3÷5/12
how can are find the domain and range of a relations
austin Reply
the range is twice of the natural number which is the domain
A cell phone company offers two plans for minutes. Plan A: $15 per month and $2 for every 300 texts. Plan B: $25 per month and $0.50 for every 100 texts. How many texts would you need to send per month for plan B to save you money?
Diddy Reply
more than 6000
For Plan A to reach $27/month to surpass Plan B's $26.50 monthly payment, you'll need 3,000 texts which will cost an additional $10.00. So, for the amount of texts you need to send would need to range between 1-100 texts for the 100th increment, times that by 3 for the additional amount of texts...
...for one text payment for 300 for Plan A. So, that means Plan A; in my opinion is for people with text messaging abilities that their fingers burn the monitor for the cell phone. While Plan B would be for loners that doesn't need their fingers to due the talking; but those texts mean more then...

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