Question

Sketch and label a graph of both an increasing and a decreasing exponential function.

Answer 1

An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:

`f(x)=a^x`

With a being a positive real, a > 0, and different from 1, a ≠ 1.

When 0 < a < 1, then the exponential function is a decreasing function and when a > 1, it is an increasing function.

For example: the function

`f(x)=2^x`

Since a = 2 > 1, the function is increasing. We have the graph below:

And the function

`f(x)=0.5^x`

Since a = 0.5 < 1, the function is decreasing. Then, the graph is: