Exponential functions > More exponential functions
12345More exponential functions

## Theory

Take a look at the applet: Exponential Functions

Every exponential function has a function rule that can be written as $f\left(x\right)=b\cdot {g}^{x}+d$.

To obtain this form you may need to use the computation rules for powers.
You can obtain the graph of $f$ by using the following transformations on $y={g}^{x}$:

• multiplication with respect to the $y$ -axis with $b$;

• translation along the $y$ -axis with $d$ units.

Therefore the graph determined by $f$ has a horizontal asymptote: the line $y=d$.
You find the potential zero by solving $b\cdot {g}^{x}+d=0$. This often requires a calculator.