### Exponential functions and logarithms: Exponential functions

### The exponential function

The exponential function

We call a function of the form \[f(x)=\blue{a}^x\] with #\blue{a}>0# an **exponential function.**

The graph is asymptotic to the #x#-axis. No matter how far left you go, #\blue{a}^x# will never be equal to #0.#

Dependent on the value of #\blue{a}#, the graph is **increasing **or **decreasing**. If #\blue{a}>1#, the graph is **increasing**. If #0<\blue{a}<1#, the graph is **decreasing.**

We note that the the entire #x#-axis is domain of the exponential function, and the range just the positive #y#-axis.

geogebra plaatje

Indicate which of the following is an exponential function.

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