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]}

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