# Math 4C Final Exam Study Guide

**Format **12 questions, some multi-part. Questions
will be similar to sample

problems in this study guide, homework problems, lecture examples or examples

from the text. The final exam is comprehensive.

**Protocol** Wednesday, December 10, 3-6 pm in YORK 2622 (tentative). No
notes nor

calculators allowed . Bring photo ID. No credit for unsupported work. No makeup

test; however lowest midterm percentage will be automatically replaced by the

final exam percentage if it is higher. Do work on final exam (blue book not

required) or attach scratch paper.

**Study Guide** Review homework, lecture notes, and notes from reading the
textbook.

Work, review sample problems below. Study with one or two other students.

Seek help at office hours; ask specific questions.

**Topics, Sample Problems**

Supp ** Expressions and functions ** 1.3.57, 69, 71, 81; 1.R.3, 5, 9

distinguish between expressions and functions

define polynomial

evaluate polynomials

perform operations on polynomials , e.g., multiplication

factor polynomials over the integers, the rationals, the reals, the complex
numbers

Supp **Rational expressions, solving equations**

evaluate and simplify rational expressions

add, subtract , multiply, and divide rational expressions

determine if a value is a solution to an equation

solve equations by inverse operations

12.7, **Partial fractions** 12.R.89; 12.T.19

12.8 determine form of partial fraction decomposition (non-repeated linear
factors,

repeated linear factors, non-repeated quadratic factors, repeated quadratic

factors)

solve partial fraction decompositions by equating coefficients or choosing

convenient values

12.2** Polynomial division** 12.R.1, 5; 12.T.5, 9

divide polynomials using long and synthetic division to find quotients and

remainders

12.3- ** Roots of polynomial equations** 12.R.13, 17, 19, 31, 37, 43, 47, 63,
67; 12.T.1, 2,

12.6 3, 4, 8, 10, 12, 14, 15, 17

use various theorems (Remainder, Factor, Linear Factors, Fundamental Theorem

of Algebra, Location or Intermediate Value, relationship between

coefficients and roots or Vieta's, Rational Roots, Upper and Lower Bound,

Descartes Rule of Signs, Conjugate Roots, Irrational Conjugate Roots) to

solve polynomial equations

5.4 **Properties of logarithms** 5.R.11, 14, 65

use properties of logarithms to find values of logarithms

use properties of logarithms to simplify or expand logarithmic expressions

5.5 **Equations involving exponents and logarithms ** 5.R.15, 35; 5.T.13

solve exponential and logarithmic equations

5.6 **Applications** 5.R.103; 5.T.6

solve compound interest problems

5.7 **Exponential growth and decay** 5.R.3, 78, 83

solve exponential growth problems

solve exponential decay problems

10.1, ** Systems of linear equations, Gaussian elimination
**

10.2 recognize when a system of linear equations has one solution, no solutions, or an

infinite number of solutions

3.1

**Functions**

determine domain, range, independent and dependent variables

3.R.1, 43, 49, 53, 102, 125; 3.T.1, 2

compute values of functions using numbers, using literals

3.R.11, 69, 73, 77, 79, 105, 114, 118; 3.T.10

compute difference quotients 3.R.5, 89, 129; 3.T.5

find slope and average rate of change, use notation 3.R.8, 13

solve application problems 3.T.17

3.2

**Graphs of functions**

use Vertical Line Test to determine if a graph represents a function

find x- and y-intercepts; positive and negative parts of graph; increasing,

decreasing, and level parts of graph; turning points (local or relative

extrema); global (absolute) extrema; slope, secant lines, and average rate

of change; concavity and (estimate) inflection points; symmetry, odd and

even functions; vertical and horizontal asymptotes; sketch graphs

3.R.10, 101, 103, 104, 107, 108, 109, 110, 111, 116, 117, 123, 124, 127,

128; 3.T.9

3.3

**Graphing transformations**

relate vertical and horizontal translations (shifts), reflections, and dilations of a

graph to its function 3.R.6, 15, 126

recognize transformations from the function

sketch graphs by applying transformations of a basic graph

3.R.9, 21, 29; 3.T.7, 8, 15

3.4

**Combining functions**

find sum , difference, product, and quotient of two functions

3.R.4ab, 81, 119; 3.T.3a

find composition of two functions

3.R.2bc, 3, 4c, 85, 86, 87, 120, 121, 122; 3.T.3bc

decompose a function 3.R.63

3.5

**Inverse functions**

know properties or inverse functions and their graphs (monotonicity, one-to-one,

Horizontal Line Test, compositions of function and its inverse)

find inverse function, if it exists, algebraically 3.R.39, 41, 91, 97, 98; 3.T.6

sketch inverse function from graph of function by reflection through y = x 3.R.7

restrict domain to find inverse function 3.R.112, 113

solve application problems 3.R.16; 3.T.16

4.1

**Linear functions**

find equations of lines in slope-intercept, point-slope, standard, and

double- intercept forms 4.R.1, 15, 19; 4.T.1

graph linear functions

find equations of lines with graphs that are parallel or perpendicular to a given

linear graph 4.R.17

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