To find points in the graph of a function you substitute the x inthe equation by specific values and find the corresponding y-value.
For the given function:
[tex]y=(\frac{1}{2})^{x-3}-8[/tex]
1. Find y when x=0
[tex]y=(\frac{1}{2})^{0-3}-8=(\frac{1}{2})^{-3}-8=\frac{1^{-3}}{2^{-3}}-8=\frac{2^3}{1^3}-8=2^3-8=8-8=0[/tex]
Point (0,0)
2. Find y when x=1
[tex]y=(\frac{1}{2})^{1-3}-8=(\frac{1}{2})^{-2}-8=\frac{1^{-2}}{2^{-2}}-8=\frac{2^2}{1^2}-8=2^2-8=4-8=-4[/tex]
Point (1,-4)
3. Find y when x=-1
[tex]y=(\frac{1}{2})^{-1-3}-8=(\frac{1}{2})^{-4}-8=\frac{1^{-4}}{2^{-4}}-8=\frac{2^4}{1^4}=2^4-8=16-8=8[/tex]
Point (-1,8)
4. Find y when x= 2
[tex]y=(\frac{1}{2})^{2-3}-8=(\frac{1}{2})^{-1}-8=\frac{1^{-1}}{2^{-1}}-8=\frac{2}{1}-8=2-8=-6[/tex]
Point (2,-6)
5. Find y when x=3
[tex]y=(\frac{1}{2})^{3-3}-8=(\frac{1}{2})^0-8=1-8=-7[/tex]
Point (3,-7)
Then, you have the next points: (-1,8), (0,0), (1,-4), (2,-6), (3,-7)
