MTH 111Z Precalculus 1: Functions

Lecture Hours: 4
Credits: 4

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.

Prerequisite: Placement into WR 115 (or higher), or completion of WR 090 (or higher); and placement into MTH 111Z (or higher), or completion of MTH 095 or equivalent course as determined by instructor; or consent of instructor or concurrent enrollment in MTH 111A (All prerequisite courses must be completed with a grade of C or better.)
Student Learning Outcomes:

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.

Statewide General Education Outcomes

Use appropriate mathematics to solve problems.
Recognize which mathematical concepts are applicable to a scenario, apply appropriate mathematics and technology in its analysis, and then accurately interpret, validate and communicate the results.

Content Outline

Function Basics
- Definition of a function
- Function notation
- Domain and range
  - Interval notation
  - Inequality notation
- Graphs of functions
  - The vertical line test
  - Increasing, decreasing, constant
  - Maximums and minimums
- Piecewise-defined functions
- Transformations of functions
  - Vertical and horizontal shifts
  - Vertical and horizontal stretches
  - Reflections
- Even and odd symmetry
- The algebra of functions
  - Sum, difference, product, and quotient of functions
  - Composition of functions
- Average rate of change
- Inverse functions
- Modeling with functions
  - Scatterplots
  - Regression
- Solving equations and inequalities involving functions
- Solving equations graphically
Power Functions
- Rational exponents and radicals
- Applications and models
Polynomial Functions
- Zeros of polynomials
- Discussion of complex numbers
- The fundamental theorem of algebra
- Applications and models
Rational Functions
- Real zeros
- Vertical asymptotes
- Removable discontinuities
- Horizontal asymptotes
- Applications and models
Exponential and Logarithmic Functions
- Exponential growth and decay
- Continuous growth and decay
- Exponential and logarithmic forms of equations
- Common and natural logarithms
- Properties of logarithms
- Applications and models