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

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Answer 1 · 2018-03-09T22:47:11

$R : [0, - \infty)$ $R:[0,-∞)$

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

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 $0$ $0$ to the conceptual $\infty$ $∞$ (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:

$R : (0, \infty)$ $R:(0,∞)$

It would look like this:

$R : [0, \infty)$ $R:[0,∞)$

Answer 2 · 2018-03-09T22:54:49

At $x = 1$ $x=1$ we have $f (x) = 0$ $f(x)=0$ As $x \to \infty$ $x->oo$ we have $f (x) \to \infty$ $f(x)->oo$

So the range is $0 \leq f (x) < \infty$ $0<=f(x)< oo$

The graph below shows the result we have reached

enter image source here

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