Lesson 10­1 Exponential Functions (done).notebook
February 16, 2016
Exponential Functions
Chapter 10 Section 1
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Lesson 10­1 Exponential Functions (done).notebook
February 16, 2016
Exponential Function
• An exponential function is a function that has a variable as an exponent.
– Examples:
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Lesson 10­1 Exponential Functions (done).notebook
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Example 1 ­ Graph
• Sketch the graph of y = 2x. Then state the function's domain and range.
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Lesson 10­1 Exponential Functions (done).notebook
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Lesson 10­1 Exponential Functions (done).notebook
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Characteristics of an Exponential Function
• In general, an equation of the form y = abx, where a ≠ 0, b > 0, and b ≠ 1, is called an exponential function with base b. Exponential functions have the following characteristics:
1. The function is continuous and one­to­one.
2. The domain is the set of all real numbers.
3. The x­axis is an asymptote of the graph.
4. The range is the set of all positive real numbers if a > 0 and all negative real numbers if a < 0.
5. The graph contains the point (0, a). (The y­
intercept is a).
6. The graphs y = abx and y = a(1/b)x are reflections across the y­axis.
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Lesson 10­1 Exponential Functions (done).notebook
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Types of Exponential Functions
• There are two types of exponential functions:
– Exponential Growth
– Exponential Decay
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Lesson 10­1 Exponential Functions (done).notebook
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Exponential Growth
• The base of an exponential growth function is a number larger than 1.
**If a > 0 and b > 1, the function y = abx represents exponential growth.
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Lesson 10­1 Exponential Functions (done).notebook
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Exponential Decay
• The base of an exponential decay function is a number between 0 and 1.
**If a> 0 and 0 < b < 1, the function y = abx represents exponential decay.
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Lesson 10­1 Exponential Functions (done).notebook
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Example 2 – Identify Exponential Growth and Decay
• Determine whether each function represents growth or decay.
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Lesson 10­1 Exponential Functions (done).notebook
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Example 3
• Simplify each expression.
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Property of Equality for Exponential Functions
• If b is a positive number other than 1, then bx = by if and only if x = y.
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Example 4 – Solve Exponential Equations • Solve each equation.
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Lesson 10­1 Exponential Functions (done).notebook
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Lesson 10­1 Exponential Functions (done).notebook
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Property of Inequality for Exponential Functions
• If b > 1, then bx > by if and only if x > y, and bx < by if and only if x < y.
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Lesson 10­1 Exponential Functions (done).notebook
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Example 5 – Solve Exponential Inequalities
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