How do you find the range of $f(x)= x/absx$ ?

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Answer 1 · 2015-09-21T00:08:39

Use $absx = { (x,if,x >= 0),(-x,if,x<0) :}$

$absx = { (x,if,x >= 0),(-x,if,x<0) :}$

So for $x > 0$ , $f(x) = x/x = 1$

For $x = 0$ , $f(x)$ is not defined#

For $x < 0$ , $f(x) = x/-x = -1$

We see that

$f(x) = x/absx = { (1,if,x > 0),(-1,if,x<0) :}$

The range of $f$ is ${-1,1}$ (not the interval, just the set of those two numbers.)

Here is the graph. There should be open circles at $(0,1)$ and $(0,-1)$

graph{y=x/absx [-10, 10, -5, 5]}

How do you find the range of f(x)= x/absxf(x)= x/absx?