# 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 = x^{2}

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

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