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Exponential functions

Exponential functions. Information. Introducing exponential functions. What can you say about this function?. Is it increasing or decreasing?. y. Does it have a constant rate?. x. Does it have any maxima or minima?. How does it behave at either end?.

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Exponential functions

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  1. Exponential functions

  2. Information

  3. Introducing exponential functions What can you say about this function? Is it increasing or decreasing? y Does it have a constant rate? x Does it have any maxima or minima? How does it behave at either end? How do you think this function is written?

  4. Exponential functions An exponential function is a function in the form: where a is a positive constant. y= ax Here are examples of three exponential functions: y = 2x y = 3x y = 0.25x In each of these examples, the x-axis forms an asymptote.

  5. Exploring exponential graphs

  6. Summary of graphs When 0 < a < 1, the graph of y = ax has the following shape: y (1, a) (1, a) x The general form of an exponential function base a is: f(x) = ax where a > 0 and a≠1 When a > 1, the graph of y = ax has the following shape: y 1 1 x In both cases the graph passes through (0, 1) and (1, a). Why does this happen?

  7. Compounding interest problems

  8. Compounding interest

  9. The number e This number denoted by e is an irrational number. e = 2.718281828459045235… (to 19 significant digits) Most scientific calculators have ex as a secondary function above the key marked “ln”. The function ex is called the exponential function or the natural exponential. This is not to be confused with an exponential function, which is any expression of the general form ax, where a is a constant.

  10. Transformations of f(x) = ex

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