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+ Exponential Growth Functions How do we graph exponential growth functions? M2 Unit 5a: Day 5

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+ Exponential Growth Function:

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+ Example: Graph the function 1 1 x01 y 1 5 Draw a smooth curve from left to right just above the x-axis that moves up and to the right. We will call functions like this parent functions because they havent been translated

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Translations in Exponential Functions. h moves the function to the right or left k moves the function up or down Example: The graph of is translated up 3 units. What is the equation of the translation? Example: The graph of is translated left 2 units and down 5 units. What is the equation of the translation?

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The graph of is translated left 3 units and down 1 unit. What is the equation of the translation? You Try:

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+ Asymptotes and y-intercepts y-intercept: To find the y-intercept, plug in zero for x. In an exponential growth function, your y-intercept is always a when your function is in the form Asymptote: a line that a graph approaches more and more closely. Exponential functions have a horizontal asymptote at y=k when your function is in the form.

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+ Example: What are the asymptote and y-intercept for the function on the left? Since this is a parent function, its asymptote is y = 0. The y-intercept is always a in a parent function, so the y-intercept is 1.

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+ Domain and Range The domain of an exponential function will always be ALL REAL NUMBERS The range of an exponential function will depend on where the asymptote is

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+ Example: Graph y = 3 x. Analyze the graph. Parent functions of exponential growth function have a horizontal asymptote at y = 0. The DOMAIN is all real numbers and the RANGE is y > 0 x01 y 1/3 1 3 1 1

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Example: Graph. Find the asymptote, domain, and range. Start by sketching the graph of. This is the parent function. Then, translate the graph __________ 2 units and __________ 2 units. right down This graph has an asymptote at the line ______________. The domain is ____________ and the range is ________________. y = -2 All Real #sy > -2 x01 y 2 6

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+ Graph the function. Find the asymptote, domain, and range. x01 y 1/4 3/21/24 The DOMAIN is all real numbers and the RANGE is y > 0 Parent functions have a horizontal asymptote at y = 0. You Try:

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+ Reflections of Exponential Functions Sometimes, you may see an exponential growth function in which a

+ Asymptote: Y-intercept: Domain: Range: Describe the translation: Describe the End Behavior: y = 1 All Real #s x01 y x012 y y > 1 As x - , f(x) 1; as x , f(x) Graph Right 1, Up 1 2

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+ Graph and analyze the function. Asymptote: Y-intercept: Domain: Range: Describe the translation: Describe the End Behavior: As x - , f(x) ___; as x , f(x) __

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+ Graph and analyze the function. Asymptote Y-intercept Domain: Range: Describe the translation: Describe the End Behavior: As x - , f(x) ___; as x , f(x) __

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+ HW: pg 122 #1-3 On pg. 122#5, 7 and pg 123 #1, 2, 4 1. Graph each function 2. Describe the translation 3. Find the asymptote 4. Find the y-int 5. Find the domain and range 6. Describe the end behavior As x - , f(x) ___; as x , f(x) __