Final Exam List of Topics

Section 1.1: Rectangular Coordinates
• Plotting points on Cartesian plane
• Distance formula
• Midpoint formula

Section 1.2: Graphs of Equations
• Intercepts
• Symmetry
• Standard form for equation of a circle

Section 1.3: Linear Equations in Two Variables
• Finding the slope between two points
• Slope-Intercept form
• Point-Slope form
• Parallel and perpendicular lines

Section 1.4: Functions
• Vertical line test
• Evaluating a function
• Piecewise functions
• Finding domain and range

Section 1.5: Analyzing Graphs of Functions
• Finding zeroes
• Increasing and decreasing
• Relative minima and maxima
• Secant line, average rate of change
• Even and odd functions

Section 1.7: Transformations of Functions
• Vertical and horizontal shifts
• Reflections
• Stretches and shrinks

Section 1.8: Combinations of Functions
• Arithmetic combinations, finding domains
• Composite functions, finding domains

Section 1.9: Inverse Functions:
• Definition
• Graph of an inverse; horizontal line test
• Finding inverse function
• Finding domain and range of an inverse function

Section 2.1: Quadratic Functions:
• Standard form
• Vertex of parabola
• Maximizing/minimizing quantities

Section 2.3: Polynomial Division
• Polynomial Division

Section 2.6: Rational Functions
• Vertical, horizontal, and slant asymptotes
• Holes

Section 2.7: Nonlinear Inequalities
• Solving a polynomial inequality
• Solving a rational inequality

Section 3.1: Exponential Functions and Their Graphs
• Graphs of basic exponential functions; Transformations
• One-to-one property

Sections 3.2: Logarithmic Functions and Their Graphs
• Evaluating logarithms
• Graphs of basic logarithmic functions; Transformations
• One-to-one property

Sections 3.3: Properties of Logarithms
• Product, quotient, and power properties
• Expanding logarithmic expressions
• Condensing logarithmic expressions

Section 3.4: Exponential and Logarithmic Equations
• Solving exponential equations
• Solving logarithmic equations

Section 4.1:Radian and Degree Measure
• Converting between radians and degrees
• Arc length
• Area of a sector of a circle

Section 4.2 and Section 4.3 : Trig Functions – Unit Circle & Right Triangles
• Definition of trigonometric functions
• Evaluating trigonometric functions
• Domain and range of sine and cosine
• Even and odd trigonometric functions
• Special angles

Section 4.4:Trigonometric Functions of Any Angle
• Quadrant angles
• Using reference angles

Section 4.5: Graphs of Sine and Cosine Functions
• Basic sine and cosine curves
• Amplitude and period
• Vertical shrinking and stretching
• Horizontal shrinking and stretching
• Reflections

Section 4.6: Graphs of Other Trigonometric Functions
• Basic tangent, cotangent, secant, and cosecant curves
• Characteristics (pg. 338)

Section 4.7: Inverse Trigonometric Functions
• Definitions of arcsin, arccos, and arctan; domain and range
• Evaluating compositions (e.g. sec[arcsin(3/5)])

Section 5.1: Using Fundamental Identities
• Trigonometric identities (pg. 374)
• Simplifying trigonometric expressions
• Trigonometric substitution

Section 5.2: Verifying Trigonometric Identities
• Guidelines (pg. 382)

Section 5.3: Solving Trigonometric Equations
• Basic techniques (e.g. like terms, factoring, square roots, etc.)
• Quadratic types
• Multiple angles

Section 5.4: Sum and Difference Formulas
• Formulas for sin (u ± v) , cos (u ± v)

Section 5.5: Double-Angle and Power-Reducing Formulas
• Formulas for sin 2u , cos 2u
• Power reducing formulas for sin² u and cos² u