Mth 103 Chapter 4 Class Notes-1

Mth 103 Chapter 4 Class Notes-1 - Page 1 (4.1) 7 6 5 4 3 2...

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Unformatted text preview: Page 1 (4.1) 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 x y 4.1 Exponential Functions (Textbook Homework: 1-17(odd), 19-24, 25, 29, 33, 39-57(odd), 65-73(odd), 87-91) Objectives: evaluating exponential function graphing exponential functions evaluating functions with base e using compound interest formulas An exponential function f with base b is defined by x b x f = ) ( or x b y = , where b > 0, b 1, and x is any real number. (Note: The variable is in the exponent.) Example 1: Determine which functions are exponential functions. For those that are not, explain why they are not exponential functions. (a) 7 2 ) ( + = x x f Yes No ______________________________________________________ (b) 2 ) ( x x g = Yes No _________________________________________________________ (c) x x h 1 ) ( = Yes No __________________________________________________________ (d) x x x f = ) ( Yes No _________________________________________________________ (e) x x h = 10 3 ) ( Yes No ______________________________________________________ (f) 5 3 ) ( 1 + = + x x f Yes No ____________________________________________________ (g) 5 ) 3 ( ) ( 1 + = + x x g Yes No __________________________________________________ (h) 1 2 ) ( = x x h Yes No ______________________________________________________ Example 2: Graph each of the following and find the domain and range for each function. (a) x x f 2 ) ( = domain: __________ range: __________ (b) x x g = 2 1 ) ( domain: __________ range: __________ Page 2 (4.1) Characteristics of Exponential Functions x b x f = ) ( b > 1 0 < b < 1 Domain: Range: Transformations of g ( x ) = b x ( c > 0) : (H S R V) V ertical: c b x g x + = ) ( (graph moves up c units) c b x g x = ) ( (graph moves down c units) H orizontal: c x b x g + = ) ( (graph moves c units left) c x b x g = ) ( (graph moves c units right) R eflection: x b x g = ) ( (graph reflects over the...
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Mth 103 Chapter 4 Class Notes-1 - Page 1 (4.1) 7 6 5 4 3 2...

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