Topic Outline

Below is our topic outline, listing the concepts in the order we will study them. If you are struggling to fully understand any of the material, this page will serve as your resource for additional support. Use it to review and reinforce your understanding of each topic as you work through the assignments.

Topical Outline 

Functions Linear and Quadratics

I.   Functions including domain, range, increasing and decreasing (Chapter 2 in Textbook)

a. Definition of a function

b. Function Notation

i. Functions expressed using function notation

ii. Evaluation of function notation from equations and graphs

c. Identifying functions given table, graph or equation form

d. Domain and range of algebraic functions

II. Linear Function (Chapter 3 in Textbook)

a. Average Rate of Change

b. Creating Linear Functions 

c. Solving Absolute Value Equations

II. Quadratic Functions (Chapter 3 in Textbook)

a. Creating Quadratic Functions

b. Application of Quadratic Functions

Functions - Transformations, Inverses and Piecewise

I. Inverse Functions

a. Combining Functions

i.      Sum difference, product, quotient of functions

ii. Composition of two functions and composition notation.

b. Inverse Functions

i. Notation of an inverse function. Definition of a one-to-one function

ii. Algebraic determination of the inverse of a function

iii.   Graphical properties, Domain and Range of an inverse function

II. Parent functions and their transformations (Chapter 2.4 in Textbook)

i.      Parent (also called base/toolbox) functions

ii.     Transformations of Functions. 

II. Piecewise functions (Chapter 2.4 in Textbook)

i. Notation and Evaluating of piecewise functions

ii.    Graphs and Domain of  piecewise functions

Exponential/Logarithmic Functions (Chapter 5 in Textbook)

I. Graphs of Exponential/Logarithmic Functions

a.      Intercepts and End behavior

b.      Domain and range

c.      Introduction to the number e

d.     Equations of asymptotes

II. Exponential/Logarithmic Equations

a. Evaluation of exponential and logarithmic expressions

b. Solving exponential and logarithmic equations

i. Conversions between exponential and logarithmic form

ii. Log Properties

iii. Extraneous solutions

III. Application of Exponential/Logarithmic Functions

 Polynomials (Chapter 4 in Textbook)

I. Behavior and roots of polynomial functions

a. End behavior of polynomial functions

b. Division of polynomials

c. Polynomials as a product of linear factors

d. Multiplicity of zeros

e. Complex zeros

II. Analysis of polynomials. 

a. Intercepts and End behavior

b. Zeros

c. Domain and range

Rational Functions (Chapter 4 in Textbook)

 I. Analysis of rational functions

a. Intercepts and End behavior

c. Domain and range

d. Equations of Asymptotes

e. Inequalities of Rational Functions. 

 Conic sections - Not in our textbook

a.      Circle

i. Definition of a circle

ii. Equation of a circle

b.      Parabola

i. Definition of a Parabola

ii. Equation of a Parabola

c.       Ellipse

i. Definition of an Ellipse

ii. Equation of an Ellipse

d.      Hyperbola

i. Definition of a Hyperbola

ii. Equation of a Hyperbola