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Lesson 8-6/8-7/8-8 Exponential Functions

Lesson 8-6/8-7/8-8 Exponential Functions

Lesson 8-6/8-7/8-8 Exponential Functions. Geometric Sequences, Exponential Equations, Exponential Growth and Decay. A look at the past…. Consider the table below… What is going on in the table? Adding 4 each time This is a linear function! y = 4x - 1. A look at TODAY….

By myra
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Exponential Functions

Exponential Functions

Exponential Functions. The exponential function f with base b is defined by f (x) = b x or y = b x Where b is a positive constant other than and x is any real number. /. Base is 2. Base is 10. Base is 3. Definition of the Exponential Function.

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Exponential Functions

Exponential Functions

Exponential Functions. Our presentation today will consists of two sections. Section 1: Exploration of exponential functions and their graphs. Section 2: Discussion of the equality property and its applications. First, let’s take a look at an exponential function.

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Exponential Functions

Exponential Functions

Exponential Functions. Section 1.3. Exponential Functions. What real-world situations can be modeled w ith exponential functions???. Rules for Exponents. The Number e. Basic Practice Problems. Graph the function. State its domain, range, and intercepts. y - int :. x - int :.

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Exponential Functions

Exponential Functions

Exponential Functions. In this section, we will study the following topics: Evaluating exponential functions with base a Graphing exponential functions with base a Evaluating exponential functions with base e Graphing exponential functions with base e. Transcendental Functions.

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Exponential Functions

Exponential Functions

Exponential Functions. The exponential function f with base b is defined by: f ( x ) = b x or y = b x Where b is a positive constant other than 1 and x is any real number. Definition of the Exponential Function. Base is 2. Base is 10. Base is 3.

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Exponential Functions

Exponential Functions

Exponential Functions. Exponential function. A linear relationship is one in which there is a fixed rate of change (slope). An exponential relationship is one in which for a fixed change in x , there is a fixed percent change in y. Percent Change.

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Exponential Functions

Exponential Functions

Exponential Functions. Basic Exponential Function. f(x)=ac bx. exponential function in base c asymptote: x-axis. a affects the vertical stretch a is also the initial value a can also flip the function. b affects the horizontal stretch b is the period.

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Exponential Functions

Exponential Functions

Exponential Functions. If a > 0, a ≠ 1, f ( x ) = a x is a continuous function with domain R and range (0, ∞ ). In particular, a x > 0 for all x . If 0 < a < 1, f ( x ) = a x is a decreasing function . If a > 1, f is an increasing function.

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Exponential Functions

Exponential Functions

Exponential Functions. Definition of Exponential Functions. The exponential function f with a base b is defined by f(x) = b x where b is a positive constant other than 1 (b > 0, and b ≠ 1) and x is any real number. So, f(x) = 2 x , looks like:. Graphing Exponential Functions.

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Exponential Functions

Exponential Functions

Exponential Functions. With your Graphing Calculator graph each of the following. y = 2 x. y = 3 x. y = 5 x. y = 1 x. Determine what is happening when the base is changing in each of these graphs. y = 3 x. y = 2 x. y = 3 x. y = 5 x. y = 2 x. y = 1 x. y = 3 x. y = 5 x. y = 2 x.

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