Section 5.1a class notes_0

Section 5.1a class notes_0 - ( ) 3 1 x f x =-can be...

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Section 5.1a Exponential Functions Objective 1: Understanding the Characteristics of Exponential Functions Definition of an Exponential Function An exponential function is a function of the form ( ) x f x b = where x is any real number and 0 b such that 1 b . The constant, b , is called the base of the exponential function. Characteristics of Exponential Functions For 0 b , 1 b the exponential function with base b is defined by ( ) x f x b = . The domain of ( ) x f x b = is ( 29 , -∞ ∞ and the range is ( 29 0, . The graph of ( ) x f x b = has one of the following two shapes ( ) x f x b = , 1 b ( ) x f x b = , 0 1 b < < The graph intersects the y- axis at ( 29 0 1 , . The graph intersects the y- axis at ( 29 0 1 , . The line 0 y = is a horizontal asymptote. The line 0 y = is a horizontal asymptote. 5.1.3 Sketch the graph of the exponential function f(x) = ______. 5.1.6 Determine the correct exponential function of the form ( ) x f x b = whose graph is given. f(x) = __________________________
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3 1 x y = - 3 x y = 1 y = - Objective 2: Sketching the Graphs of Exponential Functions Using Transformations The graph of
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Unformatted text preview: ( ) 3 1 x f x =-can be obtained by vertically shifting the graph of 3 x y = down one unit. Shift the graph of 3 x y = down one unit. 5.1.17 Use the graph of 3 x y = and transforms to sketch the exponential functions. Determine the domain and range. Also, determine the y-intercept and find the equation of the horizontal asymptote. Objective 3: Solving Exponential Equations by Relating the Bases The function ( ) x f x b = is one-to-one because the graph of f passes the horizontal line test. If the bases of an exponential equation of the form u v b b = are the same, then the exponents must be the same. The Method of Relating the Bases for Solving Exponential Equations If an exponential equation can be written in the form u v b b = , then u v = . 5.1.23, 26, and 30 Solve the exponential equation using the method of relating the bases by first rewriting the equation in the form u v b b = ....
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Section 5.1a class notes_0 - ( ) 3 1 x f x =-can be...

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