Functions and their graphs
- Graph functions using horizontal and vertical shifts
- Graph functions using compressions and stretches
- Graph functions using reflections about the x-axis or y-axis
- Form composite functions and find the domain
- Determine the inverse of a function
- Graph an inverse function from the graph of a function
Functions, polynomials, theory of equations, etc.
This course prepares students to take courses in calculus, statistics, mathematics for elementary education majors, and other areas where algebra skills are required. Fluent skills in algebra are necessary for success in any area that uses mathematical analysis. The mastery of college algebra requires well-developed skills, clear conceptual understanding, and the ability to model phenomena in a variety of settings. College Algebra develops the concepts of graphing functions, polynomial and rational functions, exponential and logarithmic functions, conic sections, solving systems of equations, the binomial theorem, permutations, combinations, and probability. This course contributes to all the expected learning outcomes of the Mathematics BS degree. For more detailed information, visit the Math 110 Wiki page.
Polynomial and Rational Functions
- Quadratic functions
- Polynomial functions
- Rational functions
- Polynomial and rational inequalities
- The real zeros of a polynomial function
- Complex zeros and the Fundamental Theorem of Algebra
- The Intermediate Value Theorem.
- The inequalities |x-a|<b and a-b<x<a+b
Exponential and Logarithmic Functions
- Exponential functions
- Logarithmic functions
- Properties of Logarithms
- Logarithmic and exponential equations
- Compound interest
- Exponential growth and decay
Systems of Equations and Inequalities
- Solve systems of linear equations using substitution and elimination. Detect systems that have infinitely many solutions or no solutions.
- Solve systems of non-linear equations using substitution and elimination, including systems with multiple solutions.
Sequences and Induction
- Find terms in a sequence using a formula and a recursive definition.
- Given terms in a sequence that follow a pattern, produce a formula for the sequence.
- Find a formula for terms in an arithmetic sequence and be able to add the terms of a finite arithmetic sequence.
- Find a formula for the terms in a geometric sequence and be able to find the sum of finite and infinite geometric series.
Counting and Probability
- Count the number of ways in which a sequence of events can occur (the Rule of Product).
- Compute probabilities based on equally likely outcomes.
- Compute probabilities of complements of events and unions of disjoint events.
- Compute the probability of a sequence of independent events.