# How do you graph y=5^x?

Jul 2, 2018

See below:

#### Explanation:

With any graph, we can make a table of values, and then plot them.

$x \textcolor{w h i t e}{a a a} | \textcolor{w h i t e}{a a a} y$

$- 3 \textcolor{w h i t e}{\frac{l}{l}} | \textcolor{w h i t e}{\frac{2}{2}} {5}^{- 3} = \frac{1}{125}$

$0 \textcolor{w h i t e}{a a a} | \textcolor{w h i t e}{a a a} {5}^{0} = 1$

$1 \textcolor{w h i t e}{a a a} | \textcolor{w h i t e}{a a a} {5}^{1} = 5$

$2 \textcolor{w h i t e}{a a a} | \textcolor{w h i t e}{a a a} {5}^{2} = 25$

$3 \textcolor{w h i t e}{a a a} | \textcolor{w h i t e}{a a a} {5}^{3} = 125$

$4 \textcolor{w h i t e}{a a a} | \textcolor{w h i t e}{a a a} {5}^{4} = 625$

Notice, as $x$ increases slowly, $y$ balloons up really quickly. This means our parabola has a very high slope for positive values.

graph{5^x [-10, 10, -5, 5]}

Hope this helps!