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the domain and range of f(x)=(e^-x)-2

  • math -

    Start with the base function: y=e^x.

    The range of y=e^x is (0, infinity).

    If you have y=e^-x, that flips the function over the y axis, which does not change the range.

    Now factor in the -2. That shifts the function down, so subtract 2 from the range: (-2, infinity)

  • math -

    Oops, forgot the domain.

    e^x exists for all real values of x, so e^-x does also.

    Therefore, the domain is (-infinity, infinity)

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