Exponential Functions Notes 6.3

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.

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

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=3 0.5 𝑥 for x = -2

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

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

Graphing Exponential Functions

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.

Graphing Exponential Functions Example 4:Graphing 𝑦=𝑎 𝑏 𝑥 when 0<b<1 Graph 𝑓 𝑥 =− 1 2 𝑥 . Compare the graph to the graph of the parent function. Describe the domain and range of f.

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 6. 𝑓 𝑥 =2 1 4 𝑥