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`.

1 2 3 4 5 -1 -2 -3 -4 -5 -6 -7 1 2 3 4 5 -1 -2 -3 -4 -5 t f(t)
Domain: All `t ≠ -2`
Range: All `f(t) ≠ 0`

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