We can determine whether or not a point falls on the graph of a function by plugging its coordinates into the function equation.
If the right side is equal to the left side, the the equation is true, and the point does fall on the graph.
We're given:
[tex]f(x)=2^x-3[/tex]
⇒ Plug in the coordinates:
[tex]1=2^3-3\\1=8-3\\1\neq5[/tex]
(3,1) is not on the graph.
[tex]f(x)=2^x-3[/tex]
⇒ Plug in the coordinates:
[tex]1=2^(0)-3\\1=1-3\\1\neq-2[/tex]
(0,1) is not on the graph.
[tex]f(x)=2^x-3[/tex]
⇒ Plug in the coordinates:
[tex]3=2^(1)-3\\3=2-3\\3\neq-1[/tex]
(1,3) is not on the graph.
[tex]f(x)=2^x-3[/tex]
⇒ Plug in the coordinates:
[tex]8=2^(6)-3\\8=64-3\\8\neq61[/tex]
(6,8) is not on the graph.
None of the points are on the graph of the given function.
