what would the range be on f(x) = -4 l x+7 l ?

Question

turingtest · Answer

what is the range on 
f(x)=|x+7|
?

anonymous · Answer

i think i'm not sure somehow my teacher got (- infinity, 0] and i have no idea what he did

turingtest · Answer

what is the range of f(x)=|anything| ?
what values can an absolute value take on?

anonymous · Answer

im sorry i'm so confused i know the domain is all reals because nothing limits it but i also thought hte range would be like all reals as well yet he gave us a diff answer so im unsure what to do

turingtest · Answer

can |x| be negative?

anonymous · Answer

noooo

turingtest · Answer

so then the range is not all reals, is it?
it can't be negative, the least it can be is zero. It can be as big as you want though by putting in larger and larger x.
so the range of f(x)=|x+7| is [0,infty) , agreed?

anonymous · Answer

well even if x is a negative number wouldnt it not matter because the absolute value makes it postivie?

turingtest · Answer

right, so that means it $$|x|\ge0$$like I said, the LEAST it can be is zero. Hence the range is from zero to positive infinity$$[0,\infty)$$
So far so good ?

anonymous · Answer

OH okay gotcha now

turingtest · Answer

now what about$$f(x)=-|x|$$if |x| is always positive, then -|x| is always negative. The MOST it can be is zero. 
We can make f(x) very negative (as negative as we want in fact)  by putting in very large negative or positive x. 
Hence the range is$$(-\infty,0]$$(I hope you see that the 7 and 4 change nothing, only the fact that the 4 is negative matters)
Make sense now?

anonymous · Answer

yes it does thank you so much you're a life saver

turingtest · Answer

happy to help :)