#### Description

MATH 115 is a preparation for Calculus, either MATH 220 (for which Math 113 is an alternate prerequisite) or MATH 140, with a focus on functions and graphs and algebraic techniques preparatory to calculus. The functions studied include polynomials, rational functions, exponential and logarithmic functions, and trigonometric functions.

(A graphing calculator such as the TI- 83, is required for Math 115. It is used in exploring the graphs of functions and equations and in solving problems.)

#### Prerequisites

Satisfactory score on Math Department placement exam, completion of the appropriate module of MATH 003, or completion of Math 113.

**Topics**

**Algebra**

Inequalities

Absolute value inequalities

Table of signs for polynomial and rational inequalities

**Functions**

Domain

Operations including compositions

Inverses

Graphs

Symmetry

Transformations: Shifts, reflections, stretching and shrinking

**Quadratic functions and equations**

Applications involving quadratic equations

Parabolas

Extreme value problems

Quadratic related equations including radical equations

**Polynomials**

Shape of graph

Writing polynomial functions with specific properties

Using a graphing calculator to draw complete graphs

**Rational functions**

Finding intercepts and asymptotes

Graphing with and without calculator

**Conic sections**

Standard equations for parabolas, circles, ellipses, and hyperbolas, shifts of conic sections

(if time allows)

**Exponential and Logarithmic functions**

Definition

Graphs

Exponent rules

Laws of logarithms

Exponential and logarithmic equations

Exponential growth and decay

**Trigonometry**

Angles

Radian and degree measurement of angles

Arc length and angular speed

**Trigonometric functions**

Circle, point, and right-triangle definitions of functions

Graphs of trig functions

Sinusoidal graphs

**Solving triangles**

Right triangles

Law of Cosines

Law of Sines

**Trigonometric identities**

Reciprocal identities

Pythagorean identities

Negative-angle identities

Periodicity identities

Sine and cosine addition and subtraction identities

Double-angle identities

Power-reducing identities

**Trigonometric equations**

Finding algebraic solutions

Finding calculator solutions