Math 4C Final Exam Study Guide

4.2 Quadratic functions
transform equations of quadratic functions among general, vertex, and factored
forms (use completing the square where appropriate)
find vertex and axis of symmetry, x- and y-intercepts, vertex of graph of quadratic
function (parabola) 4.R.2, 6, 21, 4.T.2, 5
sketch graphs using transformations of y = x²
sketch graphs using vertex, x- and y-intercepts
find discriminant and use discriminant to find number of zeros (roots)
find function from its graph
solve application problems 4.R.20, 27, 31; 4.T.6

4.5 Maximum and minimum values
find maximum and minimum values by analyzing functions containing quadratic
expressions 4.R.33, 35, 37; 4.T.12
Supp Power functions
graphs of power functions
given values, find a power function

4.6 Polynomial functions
find degree of polynomial function
relate linear factors, zeros, roots, and x-intercepts 4.R.5
use properties of graphs (continuity, smoothness, maximum number of turning
points, end behavior, behavior near x-intercepts) as aids in graphing
4.R.53, 55; 4.T.3, 10, 15

4.7 Rational functions
graph rational functions (domain, range, intercepts, asymptotes)
translations, reflections, and dilations 4.R.9, 11, 63; 4.T.13

5.1 Exponential functions
graph exponential functions (domain, range, intercepts, asymptotes)
translations, reflections, and dilations 5.T.1

5.2 Natural exponential function
graph natural exponential function (domain, range, intercepts, asymptotes)
translations, reflections, and dilations 5.R.29

5.3 Logarithmic functions
graph logarithmic functions (domain, range, intercepts, asymptotes)
translations, reflections, and dilations 5.R.77

6.1-4 Solving triangles 6.R.25, 33, 63, 67
solve right triangle applications
find area of SAS triangles

9.1 Laws of Sines and Cosines 9.R.1, 5, 7, 21
use Law of Sines to solve ASA, SAA, and SSA triangles
use Law of Cosines to solve SAS and SSS triangles
use Heron's formula to find area of SSS triangles

6.4-5, Trigonometric functions of angles 7.R.19
7.3 find values of trig functions of any angle defined by a point on the plane
find values of trig functions of any angle defined by a point on unit circle
find values of trig functions of real numbers (radians)
use properties of sine function (odd) and cosine function (even) to find
values of trig functions

7.1, 7.2 Radian measure and geometry 7.T.7
convert between radians and degrees
solve problems involving arc length and sector area
solve problems involving angular speed and linear speed

7.4, 7.5 Graphs of trigonometric functions 7.R.7, 45, 51
graph sine and cosine functions (domain, range, intercepts, asymptotes, period)
translations, reflections, and dilations (amplitude, phase shift, period)
determine amplitude, period, phase shift, vertical shift
find equation from graph of sine or cosine function

7.7 Graphs of other trigonometric functions 7.R.53a
graph tangent, cotangent, cosecant, and secant functions (domain, range,
intercepts, asymptotes, period)
translations, reflections, dilations

12.1 Complex numbers (rectangular form)
conjugates of complex numbers
complex number arithmetic (adding, subtracting, multiplying, dividing, powers,
roots) in rectangular form 12.R.71, 73, 75, 77, 79, 81c, 85; 12.T.16
plotting complex numbers in the complex plane

13.6 Complex numbers (trigonometric or polar form)
modulus and argument of complex numbers
converting between complex numbers in rectangular and trig forms 13.R.79
multiplying and dividing complex numbers in trig form 13.R.81, 83
DeMovire's theorem (finding powers and roots of complex numbers in trig form)
13.R.87, 91

6.2, Trig identities 6.R.39, 45; 7.R.37

6.5, use basic trigonometric identities to find missing values of trig functions

7.3 simplify trigonometric expressions using identities
prove trigonometric identities

8.1 Addition formulas 8.R.5, 11; 8.T.1
apply sine, cosine, and tangent addition/ subtraction formulas

8.2 Double-angle and half-angle formulas 8.R.19, 23, 27, 103a; 8.T.3
apply double-angle formulas
apply half-angle formulas

8.4 Trigonometric equations 8.R.51, 53; 8.T.5, 7
solve trigonometric equations

8.5 Inverse trig functions 8.R.83, 89; 8.T.11, 15
evaluate expressions involving inverse trigonometric functions

13.3, Sequences, Limits of Sequences 13.R.35, 46, 52, 55; 13.T.8

13.4, given a general term, write the first four terms of the sequence

13.5 given the first four terms of a sequence, find a possible general term
determine if a sequence converges or diverges (and find its limit if it converges)
find the sum of an infinite geometric sequence that converges

Supp Limits of Functions
determine if a function has a limit as x approaches infinity (and find the limit if it
exists)
determine if a function has a limit as x approaches some finite value c (and find
the limit if it exists)
determine one-sided limits, if they exist
use limits to determine if a function is continuous at a point
determine limits (if they exist) for undefined expressions (indeterminate forms)
use laws of limits to determine limits of functions

Supp Rates of Change and Graphical Interpretations
calculating average velocity of a position function
interpreting average velocity as slope of secant line of graph of a position function
finding equation of secant line through two points of a graph
estimating instantaneous velocity of a position function
interpret instantaneous velocity as slope of tangent line of graph of a position
function
finding equation of tangent line at a point of a graph

Supp Instantaneous Rate of Change and Derivative of a Function at a Point
calculate instantaneous rate of change of a function at a point using limit
definition
calculating derivative of a function at a point using limit definition
interpreting instantaneous rate of change of a function at a point as slope of
tangent line at the point
finding equation of tangent line at a point of a graph
understanding when a derivative of a function may fail to exist at a point