Question

Question #f6298

Answer 1

Range = all real #s except 0

Explanation:

Range is, in common tongue, defined as all possible outputs your function can have, given a set of inputs (your domain).

When asked what a function's range is, however, this question is not particularly useful: it's not efficient (or possible) to check every single input and see if it gives you a valid output. Therefore, a more useful question is what outputs could you NOT have for your given domain?

Given the particular function `y = 2/x`, The only thing I'm worried about `f(x)` being zero. After all, it seems to me that there's no easy way to get `f(x) = 0` without plugging in `0` itself, which is not allowed since we can't divide by 0.

We can test this by setting up an equation:

`2/x = 0`

Multiply both sides by `x`:

`2 = 0`

This is clearly wrong. Hence, it is clear that there's no value of `x` that could possibly make `f(x) = 0`. Hence, we can say that the range of `f(x)` is all real numbers except 0.

This is also particularly evident given the graph of `f(x)`:

graph{2/x [-10, 10, -5, 5]}

Notice how `f(x)` goes up and down to infinity (meaning that it can be any positive or negative number), but has an asymptote at `y = 0`, meaning that it can get awfully close, but will never equal `y = 0`.

Hope that helped :)