Sec 51-filled - Math 1310 Section 5.1 Exponential Functions...

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Unformatted text preview: Math 1310 Section 5.1 Exponential Functions The function x a x f = ) ( is the exponential function with base . a We’ll be interested in graphing exponential functions. What you already know about graphing functions using transformations will apply. We’ll look at two cases of the exponential function, 1 a and . 1 < < a For 1 a : Domain: ( 29 ∞ ∞- , Range: ( 29 ∞ , Key point: (0, 1) Horizontal asymptote: = y since → y as -∞ → x The graph of x a x f = ) ( with 1 a has this shape: For 1 < < a : Domain: ( 29 ∞ ∞- , Range: ( 29 ∞ , Key point: (0, 1) Horizontal asymptote: = y since → y as ∞ → x The graph of x a x f = ) ( with 1 < < a has this shape: We can use transformations to translate the graph of an exponential function left, right, up and down and to reflect it over either the x or the y axis. We’ll use the same order for transforming these functions as we did in Chapter 3, that is 1. Reflect over the x axis 2. Translate 3. Reflect over the y axis We’ll need to start with a method for graphing a basic function, such as . 2 ) ( x x f = Example 1:...
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Sec 51-filled - Math 1310 Section 5.1 Exponential Functions...

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