Question

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

Answer 1

`f(x)=(1/2)^(x-3)`
Put `x=-2 implies f(-2)=(1/2)^(-2-3)=(1/2)^-5=(2)^5=32`
`implies f(-2)=32`
Put `x=-1 implies f(-1)=(1/2)^(-1-3)=(1/2)^-4=(2)^4=16`
`implies f(-1)=16`
Put `x=0 implies f(0)=(1/2)^(0-3)=(1/2)^-3=(2)^3=8`
`implies f(0)=8`
Put `x=1 implies f(1)=(1/2)^(1-3)=(1/2)^-2=(2)^2=4`
`implies f(1)=4`
Put `x=2 implies f(2)=(1/2)^(2-3)=(1/2)^-1=(2)^1=2`
`implies f(2)=2`
Put `x=3 implies f(3)=(1/2)^(3-3)=(1/2)^0=(2)^0=1`
`implies f(3)=1`

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