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]}