Question

Find therange of `f(x)=|x-1|`?

Answer 1

`R:[0,-∞)`

Explanation:

The range of a graph is defined as the range of points in which the graphed function lies, in respect to the `y-"axis"`.

One way you could find the range, is to graph the function given:

graph{abs(x-1) [-3.08, 3.08, -1.54, 1.54]}

From here, we can see that the graph goes from `0` to the conceptual `∞` (no matter how far you zoom out, it will go on forever).

And because we could plug in zero and get a valid answer, we can "count" this number in the range.

So instead of it looking like such:

`R:(0,∞)`

It would look like this:

`R:[0,∞)`

Answer 2

At `x=1` we have `f(x)=0` As `x->oo` we have `f(x)->oo`

So the range is `0<=f(x)< oo`

The graph below shows the result we have reached