# How do you graph f(x) = 6^x by plotting points?

Jul 2, 2018

Here are some points we can plug in. It's best if we use whole numbers:
$\left(- 2 , \frac{1}{36}\right)$
$\left(- 1 , \frac{1}{6}\right)$
$\left(0 , 1\right)$
$\left(1 , 6\right)$
$\left(2 , 36\right)$

#### Explanation:

This is the graph:

graph{6^x [-10, 10, -2, 40]}

Make sure that the line nears the x-axis, but never actually touches it. The line will continue to sweep up as it reaches infinity, but the line will never be vertical since that would make the equation a non-function.

Jul 2, 2018

Choose values for $x$ and calculate $f \left(x\right)$ at these values, then plot the points ($x , f \left(x\right)$)

#### Explanation:

Put values for $x$ into the formula and calculate $f \left(x\right)$ at these values.

Plot the points $x , f \left(x\right)$ using the horizontal axis as $x$ and the vertical axis as $f \left(x\right)$

e.g.

$\underline{\text{ "x" " " " " } f \left(x\right)}$
$- 10 \text{ " " } 0.000021$
$- 1 \text{ " " " " } 0.1667$
$- 0.5 \text{ " " } 0.408$
$- 0.1 \text{ " " } 0.840$
$\text{ "0" " " " " } \setminus \setminus 1$
$\text{ "0.1" " " } 1.196$
$\text{ "0.5" " " } 2.45$
$\text{ "1" " " " " } \setminus \setminus 6$
$\text{ "2" " " " " } 36$
$\text{ "3" " " " " } 216$
$\text{ "4" " " } \setminus \setminus \setminus 1296$

You don't have to use all of these points
To graph some of these points you would have to choose suitable horizontal and vertical axis scales, and round the decimals to 1decimal place.
Remember if you choose to plot the higher values of $f \left(x\right)$ you will lose accuracy at the lower values.