How do you find the domain and range of g(x) = 5e^x?

1 Answer
VNVDVI
Mar 2, 2018

Domain: (-oo,oo) Range: (0,oo)

Explanation:

By default, the domain of the natural exponential function, or the values of x for which f(x)=e^x exists, is all real numbers, (-oo,oo).

The range, unless the function is reflected across the x-axis by placing a negative sign in front of e^x, is (0,oo). This is because e^x can never equal zero (hence the open interval) and can never be negative -- these are fundamental properties of the exponential function. Furthermore, e^x increases as we plug in larger and larger values of x, it goes to infinity.

Here, our function involves no negative signs; thus, our range is (0,oo). The 5 has no impact on the range whatsoever.

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