What is the domain and range for #y= -abs(x-5)#?

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Answer 1 · 2018-06-25T21:03:49

See below.

There is no restriction on #x#, so domain is:

#{x in RR}#

or

#(-oo,oo)#

By definition of absolute value:

#|x-5|>=0#

Therefore:

#-|x-5|<=0#

From this we can see that the minimum value is:

as #x->+-oo#, #color(white)(8888)-|x-5| ->-oo#

For #x=5#

#|x-5|=0#

This is the maximum value:

Range is therefore:

#{y in RR | -oo < y <=0}#

or

#(-oo,0]#

The graph of #y=-|x-5|# confirms this:

graph{y=-|x-5| [-1, 10, -5, 5]}