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Mathematics
OpenStudy (anonymous):

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

OpenStudy (turingtest):

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

OpenStudy (anonymous):

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

OpenStudy (turingtest):

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

OpenStudy (anonymous):

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

OpenStudy (turingtest):

can |x| be negative?

OpenStudy (anonymous):

noooo

OpenStudy (turingtest):

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?

OpenStudy (anonymous):

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

OpenStudy (turingtest):

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 ?

OpenStudy (anonymous):

OH okay gotcha now

OpenStudy (turingtest):

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?

OpenStudy (anonymous):

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

OpenStudy (turingtest):

happy to help :)

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