This review guide covers topics that will be on Test 3, including: 1) Evaluating composite functions and determining their domains; graphing inverse functions and finding inverses of functions. 2) Evaluating exponential and logarithmic functions, determining their domains and ranges, and graphing them with or without calculators. 3) Using properties of logarithms to evaluate expressions, write logarithmic expressions in different forms, and change between exponential and logarithmic expressions. 4) Solving exponential, logarithmic, and systems of linear and non-linear equations. 5) Finding partial fraction decompositions of rational expressions with various denominators.

1. Test 3 Review Guide
Chapter 6:
Exponential and
Logarithmic Functions

2. Composite Functions
• Evaluate a composite function.
• Determine a composite
function and find its domain
(bonus topic for test 3).

3. Inverse Functions
• Given the graph of a function, graph
the inverse function .
• Given a function, find its inverse.
• Verify that two functions are inverses
of each other.
• Determine if a function is 1-1.

4. Exponential & Logarithmic Functions
• Evaluate exponential functions.
• Know the domain and range of an exponential
function.
• *Graph an exponential function by plotting points.
• *Evaluate logarithmic functions without a calculator.
• *Determine the domain of a logarithmic function.
• *Graph a logarithmic function by plotting points.
*Note: Items indicated with an * must be done without a calculator

5. Logarithmic Properties
• Use the properties of logarithms to find
the exact value of an expression.
• Write a logarithmic expression as a sum
or difference of logarithms and vice versa.
• Use the Change-of-Base formula and a
calculator to evaluate a logarithm.

6. Exponential & Logarithmic Equations
• *Change an exponential expression to a
logarithmic expression and vice versa.
• Solve an exponential equation.
• Solve logarithmic equations.
• Solve exponential and logarithmic equation
using the properties of logarithms.

7. Test 3 Review Guide
Chapter 12:
Systems of Equations

8. Chapter 12: Systems of Equations
• Solve a system of two or three linear equations
(three equations is bonus material for test 3).
• Solve a system of two non-linear equations.
• Identify a Linear and non-Linear System
• Find the partial fraction decomposition of a
rational expression with the following
denominators.
• Two Linear Terms
• One Squared Linear Term
• A Quadratic Irreducible Term
• A combination of two of the previous (bonus material)