# MATH 117: College Algebra

Credit Hours

3

Prerequisites

Math Placement Test or MATH 100 with grade of C- or better.

Description

Inverse functions, quadratic functions, complex numbers. Detailed study of polynomial functions including zeros, factor theorem, and graphs. Rational functions, exponential and logarithmic functions and their applications. Systems of equations, inequalities, partial fractions, linear programming, sequences and series. Word problems are emphasized throughout the course.

See Course Page for additional resources.

## Textbook

S. Axler, *Algebra and Trigonometry* (packaged with WileyPLUS), 1st edition. Wiley, Hoboken (2012).

ISBN: 978-1118-08841-8.

## Common Syllabus for MATH 117

**Chapter 2.** *Combining Algebra and Geometry* [1.5 Weeks]

2.1 - (Cover very quickly.) The coordinate plane: coordinates, graphs of equations, distance formula, length, perimeter, circumference.

2.2 – (Cover very quickly.) Lines: slope, equation of a line, parallel/perpendicular lines, midpoints.

2.3 – Quadratic Expressions and Conic Sections: completing the square, quadratic formula, circles, ellipses, hyperbolas. Foci for ellipses/hyperbolas optional.

2.4 – (Cover very quickly.) Area: squares, rectangles, parallelograms, triangles, trapezoids, stretching, circles and ellipses.

**Chapter 3.** *Functions and their Graphs* [2.5 Weeks]

3.1 – Functions: definition, graphs, domain, range, tables.

3.2 – Function transformations and graphs: vertical/horizontal shifts, stretches, flips, combinations of transformations, even/odd functions.

3.3 – Composition of Functions: definition, importance of order, decomposing functions, composing 3 or more functions, transformations as functions.

3.4 – Inverse Functions: definition, one-to-one functions, domain/range of inverse functions, composition of a function and its inverse, importance of notation.

3.5 – A graphical approach to inverse functions: graph of inverse functions, horizontal line test, increasing/decreasing function, inverses via tables.

**Chapter 4.** *Polynomial and Rational Functions* [2.5 Weeks]

4.1 – Integer exponents: positive integer exponents, properties of exponents, negative integer exponents.

4.2 – Polynomials: degree, algebra of polynomials, zeros, factorization, behavior as *x* approaches positive/negative infinity, graphs.

4.3 – Rational functions: definition, algebra of rational functions, polynomial division, behavior as *x* approaches positive/negative infinity, graphs.

4.4 – Complex numbers: complex number system, arithmetic/algebra of complex numbers, conjugates, division, relation to zeros and factorization.

**Chapter 5.** *Exponents and Logarithms* [3 Weeks]?

5.1 – Exponents and exponential functions: roots, rational exponents, real exponents, exponential functions.

5.2 – Logarithms as inverses of exponential functions: logarithms with arbitrary base, common logarithms, number of digits, logarithm of a power, decay/half-life problems.

5.3 – Applications of Logarithms: logarithm of products/quotients, change of base, richter scale, decibels. Apparent magnitude and sound intensity optional.

5.4 – Exponential growth: functions with exponential growth, population growth, compound interest.

**Chapter 6.** *e and the Natural Logarithm* [2 Weeks]

6.1 – Defining *e* and ln: estimating area using rectangles, definitions of *e* and ln, properties of ln.

6.2 (Optional) – Approximations of *e* and ln, and an area formula.

6.3 – Exponential growth revisited: continuous compounding of interest, continuous growth rates, doubling time.

**Chapter 7.** *Systems of Equations* [1 Week]

7.1 – Equations and systems of equations: solving an equation, solving a system graphically, solving a system by substitution.

7.2 – Solving systems of linear equations: linear equations and number of solutions, systems of linear equations, Gaussian elimination.