# How do you graph exponential function f(x) = 3^x?

Jan 5, 2016

see explanation.

#### Explanation:

to sketch f(x) = ${3}^{x}$

choose appropriate values for x and substitute them into the function to obtain corresponding value of y. Then plot these coordinate points on squared paper.

$f \left(0\right) = {3}^{0} = 1$
$f \left(1\right) = {3}^{1} = 3$
$f \left(2\right) = {3}^{2} = 9$
$f \left(3\right) = {3}^{3} = 27$

Now you can plot the points (0 ,1 ) , (1 , 3 ) , (2 , 9 ) and (3 , 27 )

There are also negative values of x that can be considered.

Here make use of the fact that $\textcolor{red}{{a}^{-} m = \frac{1}{a} ^ m}$

$f \left(- 1\right) = {3}^{-} 1 = \frac{1}{3} ^ 1 = \frac{1}{3}$
$f \left(- 2\right) = {3}^{-} 2 = \frac{1}{3} ^ 2 = \frac{1}{9}$
$f \left(- 3\right) = {3}^{-} 3 = \frac{1}{3} ^ 3 = \frac{1}{27}$
Now you can plot the points$\left(- 1 , \frac{1}{3}\right) , \left(- 2 , \frac{1}{9}\right) \mathmr{and} \left(- 3 , \frac{1}{27}\right)$

I have included the graph of $f \left(x\right) = {3}^{x}$
graph{3^x [-10, 10, -5, 5]}