Domain: The function

f(t)=1/(t+2)

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:

0=1/(t+2)

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.

Domain: All t ≠ -2
Range: All f(t) ≠ 0