# How do you graph the exponential function f(x) =2^x?

##### 1 Answer
Jan 24, 2016

see explanation below.

#### Explanation:

By choosing suitable values for x and calculating the

corresponding value of y . Then plot the points on squared

paper. Finally draw a 'smooth' curve through them.

x=0 : $y = {2}^{0} = 1 \Rightarrow \left(0 , 1\right)$
x = 1 : $y = {2}^{1} = 2 \Rightarrow \left(1 , 2\right)$
x = 2 : $y = {2}^{2} = 4 \Rightarrow \left(2 , 4\right)$
x = 3 : $y = {2}^{3} = 8 \Rightarrow \left(3 , 8\right)$

You can use negative values of x .

$x = - 1 : y = {2}^{-} 1 = \frac{1}{2} \Rightarrow \left(- 1 , \frac{1}{2}\right)$
$x = - 2 : y = {2}^{-} 2 = \frac{1}{4} \Rightarrow \left(- 2 , \frac{1}{4}\right)$
Here is the graph of ${2}^{x}$
graph{2^x [-8.89, 8.89, -4.444, 4.444]}