Question

Find the domain and range of the exponential function h(x) = 125x.

Answer 1

H(x) = 125^x

Domain: all the real numbers (from negative infinity to infinity)

Range: all the positive real numbers.

As x decreases 125^x decreases approaching to 0. The function will never reach the value 0 but will approximate to it as x goes to negative infinity. The rate of decreasing gets lower and lower, with a limit of zero, when x becomes more and more negative.

As x increases 125^x increases indefinetely and at an increasing rate. That means that the increase is accelerated (the bigger the value of x the bigger the rate of increasing).