Prior to 1990, the performance of a student in precalculus at the University of Washington was not a predictor of success in calculus. For this reason, the mathematics department set out to create a new course with a specific set of goals in mind:

A review of the essential mathematics needed to succeed in calculus.
An emphasis on problem solving, the idea being to gain both experience and confidence in working with a particular set of mathematical tools.
This text was created to achieve these goals and the 2004-05 academic year marks the eleventh year in which it has been used. Several thousand students have successfully passed through the course.

This book is full of worked out examples. We use the the notation “Soluion.” to indicate where the reasoning for a problem begins; the symbol ?? is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you find a topic treated earlier in the course. It is also a good rough outline when it comes time to study for the final examination. The book also includes an index at the end. Finally, there is an appendix at the end of the text with ”answers” to most of the problems in the text. It should be emphasized these are ”answers” as opposed to ”solutions”. Any homework problems you may be asked to turn in will require you include all your work; in other words, a detailed solution. Simply writing down the answer from the back of the text would never be sufficient; the answers are intended to be a guide to help insure you are on the right track.

A preparation for MAT 201 and the physical sciences. Students study principles, properties, and

applications of functions and their graphs. They revisit functions introduced in MAT 107 and expand

their knowledge of them. The course focuses heavily on circular trigonometric functions and introduces

conic sections. Laboratory activities place particular emphasis on the use of functions to model real

problems. Computers and/or graphing calculators are used to enhance the study of mathematics.

Prerequisites: A grade of C- or better in MAT 107 or a score of 71 or higher on the College Level Math

placement test; ENG 090 and ENG 094 (COL 090), or satisfactory placement test scores.

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.

These instructional videos cover the Examples and Try It exercises in the OpenStax Precalculus text. Created by Brian Stonelake at Southern Oregon University.

In this task students are asked to analyze a function and its inverse when the function is given as a table of values. In addition to finding values of the inverse function from the table, they also have to explain why the given function is invertible.

This lesson integrates coding and computer science into English Language Arts for the purpose of fostering appreciation of Shakespearean wit and language and to provide students exposure to coding. Students first choose words that carry insulting connotations from a Shakespearean play and then create a program that randomly generates insults based upon those found words. Swift Playgrounds, Scratch, or Raspberry Pi are recommended resources for creating this project, and links to projects are provided for each of these platforms. Sample code and directions are provided. Students who are beginning to learn coding may complete the code while more advanced individuals may modify the program or create their own.

This lesson integrates coding and computer science into English Language Arts for the purpose of fostering appreciation of Shakespearean wit and language and to provide students exposure to coding. Students first choose words that carry insulting connotations from a Shakespearean play and then create a program that randomly generates insults based upon those found words. Swift Playgrounds, Scratch, or Raspberry Pi are recommended resources for creating this project, and links to projects are provided for each of these platforms. Sample code and directions are provided. Students who are beginning to learn coding may complete the code while more advanced individuals may modify the program or create their own.

This task requires interpreting a function in a non-standard context. While the domain and range of this function are both numbers, the way in which the function is determined is not via a formula but by a (pre-determined) sequence of coin flips. In addition, the task provides an opportunity to compute some probabilities in a discrete situation.

The task is better suited for instruction than for assessment as it provides students with a non standard setting in which to interpret the meaning of functions. Students should carry out the process of flipping a coin and modeling this Random Walk in order to develop a sense of the process before analyzing it mathematically.

In this video segment from Cyberchase, the CyberSquad learns how to read a thermometer as they try to keep their chocolate sculpture from melting.

This Remote Learning Plan was created by Jennifer Gier in collaboration with Tyler Cronin and Craig Hicks as part of the 2020 ESU-NDE Remote Learning Plan Project. Educators worked with coaches to create Remote Learning Plans as a result of the COVID-19 pandemic.The attached Remote Learning Plan is designed for Grades 7-12 math students. Students will learn to perform compositions of functions algebraically. This Remote Learning Plan addresses the following NDE Standard: 11.2.2m.It is expected that this Remote Learning Plan will take students 90 minutes to complete.Here is the direct link to the Google Slide: https://docs.google.com/presentation/d/1SUxq2GPuTMEjAU54d5_b8NehjR0ArSFAP6MV119p2OU/edit?usp=sharing 

This Remote Learning Plan was created by Jennifer Gier in collaboration with Tyler Cronin and Craig Hicks as part of the 2020 ESU-NDE Remote Learning Plan Project. Educators worked with coaches to create Remote Learning Plans as a result of the COVID-19 pandemic.The attached Remote Learning Plan is designed for Grades 7-12 math students. Students will learn to identify functions and evaluate functions at a given value using function notation. This Remote Learning Plan addresses the following NDE Standard: 11.2.1a, 11.2.1bIt is expected that this Remote Learning Plan will take students 140 minutes to complete.Here is the direct link to the Google Slide: https://docs.google.com/presentation/d/1eBIpImvKMWaAZNwdJMH7chKmAxYGGFVlHCgm2kT3rc0/edit?usp=sharing 

This Remote Learning Plan was created by Jennifer Gier in collaboration with Tyler Cronin and Craig Hicks as part of the 2020 ESU-NDE Remote Learning Plan Project. Educators worked with coaches to create Remote Learning Plans as a result of the COVID-19 pandemic.The attached Remote Learning Plan is designed for Grades 7-12 math students. Students will learn to identify and create inverse functions algebraically and graphically. This Remote Learning Plan addresses the following NDE Standard: 11.2.1hIt is expected that this Remote Learning Plan will take students 90 minutes to complete.Here is the direct link to the Google Slide: https://docs.google.com/presentation/d/1Jp2zJ3gAt4VqOFCJc1z3vk7Zr0hstKgGhgsqDnbBHDw/edit?usp=sharing 

In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable.

The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real world problem with ties to developing financial literacy skills.

Students play the boardgame Robot Turtles again, this time focusing on puzzles whose solutions involve lots of repeated steps.
Students create “functions” using sets of cards and use the Function Frog card to call their functions. They consider named functions and name their own functions.
Students reflect on what functions are, why programmers use them, and how functions are different from loops.

RocketModeler was developed at the NASA Glenn Research Center in an effort to foster hands-on, inquiry-based learning in science and math. RocketModeler is a simulator that models the design and flight of a model rocket. The program works in two modes: Design Mode or Flight Mode. In the Design Mode, you can change design variables including the size of the rocket body, the fins, and the nose cone. You can also select different materials for each component. You can select from a variety of standard solid rocket engines. The program computes the center of gravity and pressure for your rocket and determines the stability. When you have a design that you like, you can switch to the Flight Mode (shown below), where you can launch your rocket and observe its flight trajectory. You can pause at any time to record data and then continue the flight through parachute deploy and recovery. This program has recently (Oct 8, 2004) been upgraded to support stomp rockets, bottle rockets, and ballistic shells in addition to solid model rockets. It also supports both English and metric units.

The task provides an opportunity for students to engage in Mathematical Practice Standard 4: Model with mathematics.