# Question #7bbc6

Jun 11, 2017

Socratic has scratchpads with a graphing feature.
www.desmos.com/calculator is a free online graphing calculator.

#### Explanation:

When your scratchpad is in edit mode, the tool bar has a graphing feature that is the same as the graphing feature in answer a question mode. I have graphed ${2}^{x}$, below:

graph{2^x [-10, 10, -5, 5]}

For the bases other than e and 10, you must use the base conversion formula ${\log}_{b} \left(x\right) = \ln \frac{x}{\ln} \left(b\right)$ or ${\log}_{b} = {\log}_{10} \frac{x}{\log} _ 10 \left(b\right)$

In the graphed, below, I have graphed ${\log}_{2} \left(x\right)$ by entering $\ln \frac{x}{\ln} \left(2\right)$

graph{ln(x)/ln(2) [-10, 10, -5, 5]}

If you must graph by hand here are a few order pairs:

For ${2}^{x}$: $\left(- 3 , \frac{1}{8}\right) , \left(- 2 , \frac{1}{4}\right) , \left(- 1 , \frac{1}{2}\right) , \left(0 , 1\right) , \left(1 , 2\right) , \left(2 , 4\right) , \mathmr{and} \left(3 , 8\right)$
For ${\log}_{2} \left(x\right)$: $\left(\frac{1}{8} , - 3\right) , \left(\frac{1}{4} , - 2\right) , \left(\frac{1}{2} , - 1\right) , \left(1 , 0\right) , \left(2 , 1\right) , \left(4 , 2\right) , \mathmr{and} \left(8 , 3\right)$