# How do you make a table to graph f(x)=(1/2)^(x -3)?

Dec 29, 2015

$f \left(x\right) = {\left(\frac{1}{2}\right)}^{x - 3}$
Put $x = - 2 \implies f \left(- 2\right) = {\left(\frac{1}{2}\right)}^{- 2 - 3} = {\left(\frac{1}{2}\right)}^{-} 5 = {\left(2\right)}^{5} = 32$
$\implies f \left(- 2\right) = 32$
Put $x = - 1 \implies f \left(- 1\right) = {\left(\frac{1}{2}\right)}^{- 1 - 3} = {\left(\frac{1}{2}\right)}^{-} 4 = {\left(2\right)}^{4} = 16$
$\implies f \left(- 1\right) = 16$
Put $x = 0 \implies f \left(0\right) = {\left(\frac{1}{2}\right)}^{0 - 3} = {\left(\frac{1}{2}\right)}^{-} 3 = {\left(2\right)}^{3} = 8$
$\implies f \left(0\right) = 8$
Put $x = 1 \implies f \left(1\right) = {\left(\frac{1}{2}\right)}^{1 - 3} = {\left(\frac{1}{2}\right)}^{-} 2 = {\left(2\right)}^{2} = 4$
$\implies f \left(1\right) = 4$
Put $x = 2 \implies f \left(2\right) = {\left(\frac{1}{2}\right)}^{2 - 3} = {\left(\frac{1}{2}\right)}^{-} 1 = {\left(2\right)}^{1} = 2$
$\implies f \left(2\right) = 2$
Put $x = 3 \implies f \left(3\right) = {\left(\frac{1}{2}\right)}^{3 - 3} = {\left(\frac{1}{2}\right)}^{0} = {\left(2\right)}^{0} = 1$
$\implies f \left(3\right) = 1$

Now plot these values on graph paper and you will get the curve of the equation.