Domain: The function
is not defined for t = -2, as this value would result in division by zero. (There would be a 0 on the bottom of the fraction.)
Hence the domain of f(t) is
"all real numbers except -2"
Range: No matter how large or small t becomes, f(t) will never be equal to zero.
[Why? If we try to solve the equation for 0, this is what happens:
Multiply both sides by (t + 2) and we get
`0 = 1`
This is impossible.]
So the range of f(t) is
"all real numbers except zero".
We can see in the graph that the function is not defined for `t = -2` and that the function (the y-values) takes all values except `0`.
Easy to understand math videos: MathTutorDVD.com