Final Topics for 2014
Chapter 3
3.4 – Graphing Polynomials

End Behavior

Factoring

Determine if the Sign of 𝑓(𝑥) is positive or negative
Chapter 4
4.1 – Inverse Functions


One-to-One Functions
Horizontal Line Test

If 𝑓(𝑥) is a one-to-one function and (𝑓°𝑔)(𝑥) = 𝑥 𝑎𝑛𝑑 (𝑔°𝑓)(𝑥) = 𝑥 then g is the inverse function of 𝑓(𝑥).

Finding the equation of the inverse of 𝑦 = 𝑓(𝑥).
o Interchange x and y. o Solve for y. o Replace y with 𝑓
−1 (𝑥).

Graphing the inverse. o Create an x/y table find points for 𝑓(𝑥).
o Interchange x and y points to graph inverse function.
4.2 – Exponential Functions

Compound Interest 𝐴 = 𝑃(1 + 𝑟 𝑛
) 𝑡𝑛

Graphing exponential functions o 𝑓(𝑥) = 𝑎 𝑥 , 𝑎 > 1 is increasing. o 𝑓(𝑥) = (
1 𝑎
) 𝑥
, 0 < 𝑎 < 1 is decreasing. o Label the x – intercept and the horizontal asymptote.
4.3 – Logarithmic Functions

Equivalent statements written in both logarithmic and exponential forms.

Solving Logarithmic Equations using exponential form.

Graph Logarithmic Functions o 𝑓(𝑥) = log 𝑎 𝑥 , 𝑎 > 1, 𝑖𝑠 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔.
o 𝑓(𝑥) = log 𝑎 𝑥 , 0 < 𝑎 < 1, 𝑖𝑠 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔.
o Label the y – intercepts and the vertical asymptote. o Logarithmic Properties

Product Property: log 𝑎

Quotient Property: log 𝑎 𝑥𝑦 = log 𝑎 𝑥 𝑦
= log 𝑎 𝑥 + log 𝑥 − log 𝑎 𝑎 𝑦 𝑦

Power Property: log 𝑎 𝑥 𝑟
= 𝑟 log 𝑎 𝑥
4.4 – Evaluating Logarithms and the Change-of-Base Theorem
 log 𝑥 = log
10
 ln 𝑥 = log 𝑒 𝑥 𝑥


Change-of-Base Theorem: log 𝑎 𝑥 = log 𝑏 log 𝑏 𝑥 𝑎
4.5 – Exponential and Logarithmic Equations

Solving an exponential equation

Solving an exponential equation using natural logarithms

Solving base e exponential equations

Solving a logarithmic equation
Chapter 5
5.1 – Angles

Finding the complement and the supplement of an angle.

Calculating with Degrees, Minutes, and Seconds.

Converting between Decimal Degrees and DMS.

Finding Positive Co-Terminal Angles.
5.2 – Trigonometric Functions


 sin 𝜃 = cos 𝜃 = tan 𝜃 = 𝑦
reciprocal to Sine csc 𝜃 = 𝑟 𝑟 𝑦 𝑥 𝑟 𝑦
reciprocal to Cosine sec 𝜃 =
reciprocal to Tangent cot 𝜃 = 𝑥 𝑟 𝑥 𝑥 𝑦

Find the exact value of the trigonometric function given a point.

Find the exact value of the trigonometric function of Quadrantal Angles.
5.3
- Evaluating Trigonometric functions using Special Right Triangles o 30°, 60°, 90° - Leg √3 is adjacent to 30° and Leg 1 is adjacent to 60° and hypotenuse is 2. o 45°, 45°, 90° - Leg 1 is adjacent to 45° and hypotenuse is √2 . o SOH, CAH, TOA

Function trigonometric function value using reference angles.
5.4
– Solving Right Triangles

Solving right triangles given an angle and a side.

Solving right triangles given two sides.

Solving a geometric problem using special right triangles.
Chapter 6
6.1 – Radian Measure

Converting Between Degrees and Radians

Arc Length

Area of a Section of a Circle
6.2 – The Unit Circle

Finding the exact trigonometric function using the unit circle.