Question

How do you find the domain and range for `y=2x-10`?

Answer 1

The domain and range are both `RR` (all real numbers).

Explanation:

The domain consists of all possible valid `x`-values, while the range consists of all possible `y`-values.

As `2x-10` is defined for all real numbers, the domain of `2x-10` is `RR`.

We would have to limit our domain if there was the possibility of dividing by `0` such as in `1/x` for `x=0`, taking an even root of a negative number, such as `sqrt(x)` for `x<0`, or taking the logarithm of a non-positive number, such as `ln(x)` for `x <= 0`. As none of these apply, we do not have any restrictions on our choice of `x`.

Note that `2((y+10)/2)-10 = y`, and thus for any real `y`, we may choose `x = (y+10)/2` to get `y = 2x-10`. As such, every real number `y` is in the range of the function.