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Graphing an Exponential Function Where a>1 

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1.) Make a table of a few (the book uses seven) values of x, and corresponding values of y. 2.) Plot the points and draw a smooth curve through them 


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If rsubscrpt1, rsubscrpt2, rsubscrpt3, etc leads to r... 

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Then a^rsubscrpt1, a^rsubscrpt2, etc leads to a^r 


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When a>1 your graph... [Exponential Growth] 

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Is an increasing function 


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When a is greater than zero and less than 1, or a^(x), then... [Exponential Decay] 

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the graph of the curve is reflected across the xaxis 


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Is a reflection about the yaxis 


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When the absolute value of a is less than one... 

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Then you have a horizontal stretch when.. af(x) 


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The parent graph of an exponential function always hits the yaxis at... 

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Exponential functions have horizontal asymptotes but not.... 

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Vertical or Oblique Asymptotes 


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How do you find f(x), when given two points? 

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1.) Think of it as f(x)=Ca^x, in which C is your constant. 2.) If one of your points is (0,1), then that point represents your constant in the form f(0)=1. 3.) With that knowledge you can say that your other point explains the function, so let's say that the other point is (2,16). That would mean your function is f(2)=16, which means a^2=16 which means that a=4. 4.) And that is Your Answer 


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g(x)=e^x, in which e is defined as [Natural Exponential Function] 

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The horizontal asymptote of f(x) 


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Continuous Compound Interest Formula 

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