# How do you graph f(x)=(1/2)^x -3 by plotting points?

Apr 27, 2017

Pick values for $x$ that are easy to solve

#### Explanation:

So we can choose the following $x$ values:
$x = - 3 , - 2 , - 1 , 0 , 1 , 2$

Plugging in the values we get the following
$f \left(- 3\right) = \setminus \frac{{2}^{3}}{{1}^{3}} - 3 = {2}^{3} - 3 = 8 - 3 = 5$
$f \left(- 2\right) = \setminus \frac{{2}^{2}}{{1}^{2}} - 3 = {2}^{2} - 3 = 4 - 3 = 1$
$f \left(- 1\right) = \setminus \frac{{2}^{1}}{{1}^{1}} - 3 = {2}^{1} - 3 = 2 - 3 = - 1$
$f \left(0\right) = \setminus \frac{{1}^{0}}{{2}^{0}} - 3 = 1 - 3 = - 2$
$f \left(1\right) = \setminus \frac{{1}^{1}}{{2}^{1}} - 3 = \setminus \frac{1}{2} - 3 = - \setminus \frac{5}{2}$
$f \left(2\right) = \setminus \frac{{1}^{2}}{{2}^{2}} - 3 = \setminus \frac{1}{4} - 3 = - \setminus \frac{11}{4}$

You can plug in the points $\left(- 3 , 5\right) , \left(- 2 , 1\right) , \left(- 1 , - 1\right) , \left(0 , - 2\right) , \left(1 , - 2.5\right) , \left(2 , - 2.75\right)$ to get
graph{(1/2)^x-3 [-14.85, 10.46, -3.99, 8.67]}