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

Mar 9, 2018

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 $y - \text{axis}$.

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,∞)

At $x = 1$ we have $f \left(x\right) = 0$ As $x \to \infty$ we have $f \left(x\right) \to \infty$

So the range is $0 \le f \left(x\right) < \infty$

The graph below shows the result we have reached