# Precalculus I: Functions

- Course Number:
- MTH 111Z
- Transcript Title:
- Precalculus I: Functions
- Created:
- Aug 15, 2022
- Updated:
- Apr 28, 2023
- Total Credits:
- 4
- Lecture Hours:
- 30
- Lecture / Lab Hours:
- 20
- Lab Hours:
- 0
- Satisfies Cultural Literacy requirement:
- No
- Satisfies General Education requirement:
- Yes
- Grading Options
- A-F, P/NP, Audit
- Default Grading Options
- A-F
- Repeats available for credit:
- 0

## Course Description

Prepares students for trigonometry or calculus, focusing on functions and their properties, including polynomial, rational, exponential, logarithmic, piecewise-defined, and inverse functions. Explores topics symbolically, numerically, and graphically in real-life applications and interpreted in context. Emphasizes skill building, problem-solving, modeling, reasoning, communication, connections with other disciplines, and the appropriate use of present-day technology. Prerequisite: MTH 95 or equivalent placement. Prerequisite/concurrent: WR 121 or WR 121Z. Audit available.

## Course Outcomes

Upon successful completion students should be able to:

- Explore the concept of a function numerically, symbolically, verbally, and graphically and identify properties of functions both with and without technology.
- Analyze polynomial, rational, exponential, and logarithmic functions, as well as piecewise-defined functions, in both algebraic and graphical contexts, and solve equations involving these function types.
- Demonstrate algebraic and graphical competence in the use and application of functions including notation, evaluation, domain/range, algebraic operations & composition, inverses, transformations, symmetry, rate of change, extrema, intercepts, asymptotes, and other behavior.
- Use variables and functions to represent unknown quantities, create models, find solutions, and communicate an interpretation of the results.
- Determine the reasonableness and implications of mathematical methods, solutions, and approximations in context.

## Alignment with Institutional Learning Outcomes

- Major
- 1. Communicate effectively using appropriate reading, writing, listening, and speaking skills. (Communication)
- Major
- 2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving)
- Major
- 3. Extract, interpret, evaluate, communicate, and apply quantitative information and methods to solve problems, evaluate claims, and support decisions in their academic, professional and private lives. (Quantitative Literacy)
- Not Addressed
- 4. Use an understanding of cultural differences to constructively address issues that arise in the workplace and community. (Cultural Awareness)
- Minor
- 5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility)

To establish an intentional learning environment, Institutional Learning Outcomes (ILOs) require a clear definition of instructional strategies, evidence of recurrent instruction, and employment of several assessment modes.

### Major Designation

- The outcome is addressed recurrently in the curriculum, regularly enough to establish a thorough understanding.
- Students can demonstrate and are assessed on a thorough understanding of the outcome.
- The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

### Minor Designation

- The outcome is addressed adequately in the curriculum, establishing fundamental understanding.
- Students can demonstrate and are assessed on a fundamental understanding of the outcome.
- The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

## Suggested Outcome Assessment Strategies

The determination of assessment strategies is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: writings (journals, self-reflections, pre writing exercises, essays), quizzes, tests, midterm and final exams, group projects, presentations (in person, videos, etc), self-assessments, experimentations, lab reports, peer critiques, responses (to texts, podcasts, videos, films, etc), student generated questions, Escape Room, interviews, and/or portfolios.

## Course Activities and Design

The determination of teaching strategies used in the delivery of outcomes is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: lecture, small group/forum discussion, flipped classroom, dyads, oral presentation, role play, simulation scenarios, group projects, service learning projects, hands-on lab, peer review/workshops, cooperative learning (jigsaw, fishbowl), inquiry based instruction, differentiated instruction (learning centers), graphic organizers, etc.

## Course Content

**Outcome #1:** Explore the concept of a function numerically, symbolically, verbally, and graphically and identify properties of functions both with and without technology.

- Given a set of data transform this information into different models.
- Identify the domain and range of a given model.
- Identify various aspects of the function

**Outcome #2:** Analyze polynomial, rational, exponential, and logarithmic functions, as well as piecewise-defined functions, in both algebraic and graphical contexts, and solve equations involving these function types.

- Create appropriate mathematical models given 2 points.
- Recognize when different functions are being asked for, exponential vs linear.
- Create appropriate mathematical models (equations) given a graph.
- Describe the various features of the function:
- Domain
- Range
- Inflections
- Concavity
- Increase/decrease

**Outcome #3:** Demonstrate algebraic and graphical competence in the use and application of functions including notation, evaluation, domain/range, algebraic operations & composition, inverses, transformations, symmetry, rate of change, extrema, intercepts, asymptotes, and other behavior.

- Interval notation
- Set notation.
- Appropriate function notation
- Construct and interpret graphical displays.

**Outcome #4:** Use variables and functions to represent unknown quantities, create models, find solutions, and communicate an interpretation of the results.

- Identify the appropriate function to use for a given problem based on context.
- Create and solve problems using linear functions.
- Create and solve problems using exponential functions:
- Decay
- Growth
- Newton’s law of cooling
- Compound interest

**Outcome #5:** Determine the reasonableness and implications of mathematical methods, solutions, and approximations in context.

- Use a variety of methods to solve real world problems
- Compare solutions and determine the reasonableness based on the problem.

## Suggested Texts and Materials

Lippman, D. & Rasmussen,M. *Precalculus 1: An Investigation of Functions,* Edition 2.2. The text is open source and available online at: https://www.opentextbookstore.com/precalc/2.2/Precalc1.pdf

## Department Notes

Word problems are to be answered using complete sentences and include appropriate units.