Math Functions

Write two equations to represent the same exponential function with a y-intercept of 5 and an asymptote at y=3 . Investigate whether other exponential functions have the same properties. Use the transformations to explain your observations.

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  1. You know that y=e^x goes through (0,1) and has an asymptote at y=0, so,
    y = e^x + 3 has its asymptote at y=3.
    Further, 5e^x goes through (0,5), so one function would be

    5e^x + 3

    Now, you can pick any number greater than 1, and the above statements hold true, so

    5*2^x, 5*10^x all do the same.

    In fact, that also means that

    5*12^7x, 5*1.001^100x all do it to.

    Since a*b^(kx) = a*e^((k lnb) x)

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  2. This is incorrect

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