MATH 19500: Precalculus

Career: Undergraduate
Category: Regular
Term Offered: Fall, Spring, Summer
Pre-requisites: C or better in Math 19000
Hours/Credits: 3 HR/WK; 3 CR
Date Effective: Fall 2026
Course Supervisor: David

Catalog Description

This course extends the study of algebra and introduces key concepts of precalculus. Topics include functions and their properties, domains and ranges, composition, transformations, and inverse functions, emphasizing graphing and analyzing polynomial, rational, exponential, logarithmic, and trigonometric functions, as well as solving related equations. It also covers trigonometric identities, trigonometric equations, conic sections, and systems of nonlinear equations. (Prerequisite for either first term calculus course Math 20100 or 20500.)

Text

Algebra and Trigonometry, 2nd Edition, and Intermediate Algebra (Chapter 11)

Schedule

Course Learning Outcomes

After successfully completing this course, students should be able to:

1. Use function notation and analyze functions represented algebraically, graphically, numerically, and verbally, including evaluating functions and determining domain, range, intercepts, intervals of increase or decrease, and average rate of change. a, b, e1, e2

2. Determine whether a relation represents a function and whether a function is one-to-one, using the vertical and horizontal line tests and appropriate algebraic methods. a, b, e1, e2

3. Perform operations on functions and analyze transformations, compositions, and inverse functions, translating between algebraic and graphical representations. a, b, e2

4. Graph and analyze linear, absolute value, quadratic, polynomial, rational, and radical functions, identifying important features such as intercepts, extrema, zeros, asymptotes, end behavior, and domain and range. a, b, e2

5. Analyze polynomial and rational functions algebraically, including polynomial division, determining zeros of polynomial functions, and relating algebraic properties to graphical behavior. a, b, e2

6. Solve equations and inequalities involving the functions studied in the course, including polynomial, rational, radical, exponential, logarithmic, and trigonometric equations, using appropriate algebraic and graphical methods. a, b, e2

7. Graph and analyze exponential and logarithmic functions and use their properties to solve equations and model applications, including exponential growth and decay. a, b, c, e2

8. Use angles, right-triangle trigonometry, and the unit circle to evaluate and interpret trigonometric functions, including sine, cosine, tangent, and the other trigonometric functions. a, b, e1, e2

9. Graph and analyze trigonometric and inverse trigonometric functions, identifying characteristics such as amplitude, period, phase shift, domain, and range when appropriate. a, b, e2

10. Apply trigonometric identities and formulas, including fundamental identities, sum and difference identities, and double-angle and half-angle formulas, to simplify expressions and solve trigonometric equations. a, b, e1, e2

11. Use quadratic and other functions to solve optimization and modeling problems, including determining maximum and minimum values and interpreting their meaning in context. a, b, c

12. Write, graph, and analyze equations of conic sections, including circles and ellipses, and identify their key geometric features from their equations. a, b, e1, e2

13. Solve systems of nonlinear equations using algebraic and graphical methods and interpret the solutions as points of intersection.a, b, e2

14. Apply appropriate precalculus concepts to formulate and solve mathematical and real-world problems and communicate solutions using correct mathematical notation, algebraic reasoning, and graphical representations.a, b, c, g

Course Assessment Tools

1. Term average, based primarily on homework, in-class quizzes, and in-class examinations: 60% of the course grade.

2. Comprehensive written final examination: 40% of the course grade.

Departmental Learning Outcomes

The mathematics department, in its varied courses, aims to teach students to:

a. Perform numeric and symbolic computations.
b. Construct and apply symbolic and graphical representations of functions.
c. Model real-life problems mathematically.
d. Use technology appropriately to analyze mathematical problems.
e. State (e1) and apply (e2) mathematical definitions and theorems.
f. Prove fundamental theorems.
g. Construct and present (generally in writing, but occasionally orally) a rigorous mathematical argument.