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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 x-axis |
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| Is a reflection about the y-axis |
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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 y-axis 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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