1. Exponential Functions
Notes 6.3

2. Identifying & Evaluating Exponential Functions
An exponential function is a nonlinear function of the form 𝑦=𝑎 𝑏 𝑥 , where 𝑎≠0, 𝑏≠1, and 𝑏>0. As the independent variable x changes by a constant amount, the dependent variable y is multiplied by a constant factor.

3. Identifying & Evaluating Exponential Functions
Example 1: Identifying Functions
Does each table represent a linear or an exponential function? Explain.

4. Identifying & Evaluating Exponential Functions
Example 2: Evaluating Exponential Functions
Evaluate each function for the given value of x.
 a. 𝑦=−2 5 𝑥 for x = 3
b. 𝑦= 𝑥 for x = -2

5. Evaluating Expressions with Rational Exponents
You Try!
Does the table represent a linear or an exponential functions? Explain.

6. Evaluating Expressions with Rational Exponents
You Try!
Evaluate the function when x = -2, 0, and 1/2.

7. Graphing Exponential Functions

8. Graphing Exponential Functions
Example 3:Graphing 𝑦=𝑎 𝑏 𝑥 when b>1
Graph 𝑓 𝑥 =4 2 𝑥 . Compare the graph to the graph of the parent function. Describe the domain and range of f.

9. Graphing Exponential Functions
Example 4:Graphing 𝑦=𝑎 𝑏 𝑥 when 0<b<1
Graph 𝑓 𝑥 =− 𝑥 . Compare the graph to the graph of the parent function. Describe the domain and range of f.

10. Graphing Exponential Functions
You Try!
Graph the function. Compare the graph to the graph of the parent function. Describe the domain and range of f.
5. 𝑓 𝑥 =−2 4 𝑥 𝑓 𝑥 = 𝑥