Transcript title

Precalculus I: Functions

Credits

4

Grading mode

Standard letter grades

Total contact hours

40

Lecture hours

40

Prerequisites

MTH 095 or higher (except MTH 098, MTH 102, MTH 105Z, MTH 244, and STAT 243Z) or minimum placement Math Level 18.

Course Description

A course primarily designed for students preparing for trigonometry or calculus. This course focuses on functions and their properties, including polynomial, rational, exponential, logarithmic, piecewise-defined, and inverse functions. These topics will be explored symbolically, numerically, and graphically in real life applications and interpreted in context. This course emphasizes skill building, problem solving, modeling, reasoning, communication, connections with other disciplines, and the appropriate use of present-day technology.

Course learning outcomes

1. Explore the concept of a function numerically, symbolically, verbally, and graphically and identify properties of functions both with and without technology.
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.
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.
4. Use variables and functions to represent unknown quantities, create models, find solutions, and communicate an interpretation of the results.
5. Determine the reasonableness and implications of mathematical methods, solutions, and approximations in context.

Content outline

1. Solve Equations Using Graphing Technology
2. Functions (includes algebraic form, graphic form, tabular form)
   1. Evaluating functions
   2. Average Rate of Change
   3. Domain and Range
   4. Graphs of Functions
   5. Transformations
   6. Inverse Functions
   7. Function Algebra and Composition of Functions
3. Exponential Functions and Exponential Equations (includes algebraic form, graphic form, tabular form)
4. Logarithms and Logarithmic Equations (includes algebraic form, graphic form, tabular form)
5. Rational Functions and Equations
6. Polynomial Functions
   1. Roots and multiplicities
   2. General graph shape and end behavior
7. Mathematical Modeling / Applications
   1. Creating and using mathematical models
8. Writing and Working in a Group

Required materials

Students are required to have a license for web-based software which includes an e-text. Paper copy of the textbook is optional.

General education/Related instruction lists

• Science not Lab
• Mathematics