Question

How do you find the domain and range of `f(x)=3x+2`?

Answer 1

Both domain and range are every real number

Explanation:

The domain is every value of `x` you can put into the function that will output a valid `y` value.

When doing this we usually make sure to keep to the real numbers, and just check for values that will make the function "break", e.g.: will make us divide by zero, have a negative number under a root, have a zero or negative number in a logarithm, etc.

Lines like this, can take every value of `x` we want, so the Domain is every real number

`D = -oo < x < oo | x in RR`

The range is every value of `y` the function can take. Normally this only matters is case like quadratics, where we can't have a negative number, or like wave functions that will never be bigger than their amplitudes.

Once more, lines can output every number between negative infinity and infinity, so the range is the same as the domain in this case

`I = -oo < x < oo | x in RR`