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# Plz help- Write the expression f(x)=|x−2|+|x−16|f(x)=|x−2|+|x−16| without absolute values symbols is xx is in each of the given

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Write the expression f(x)=|x−2|+|x−16| without absolute values symbols is x is in each of the given intervals.

(−∞,2]: f(x)=

[2,16]: f(x)=

[16,∞): f(x)=

Feb 1, 2019
edited by Roxettna  Feb 1, 2019

#1
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I think that this is what you mean

f(x)=|x−2|+|x−16|

When x is less then 2 then  x-2 and x-16  will both be negative SO

f(x)= 2-x+16-x = 18-2x

When x is between 2 and 16  x-2 will be positive and x-16 will be negative SO

f(x)=x-2+16-x = 14

When x is greater than 16   both expressions will be positive   SO

f(x)=x-2+x-16 = 2x-18

Feb 1, 2019
#2
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Thank you very much! I had already solved the [2,16]: f (x)= 14 but for some reason I couldn't put my head around the other two! Is there any suggestions you can give in order to remember the steps easier? I always freeze when this comes up in any quiz

Roxettna  Feb 1, 2019
#3
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Mmm

Well I could see that the key numbers were going to be 2 and 16  can you see why?

I actually draw a rough number line and marked 2 and 16 on it.  Then I had to work out each of the 3 sections seperately.

for instance.

try x=0     x-2=-2   so  |x-2|  must be  -(x-2) which is 2-x        at x=0 x-16 is already positive so  |x-16|=x-16

So when x is less than 2   the value will  be  2-x   +  x-16  etc.

Do you understand that?

You just need to think about that for each of the 3 sections of the graph and you will have your full answer.

Melody  Feb 1, 2019
edited by Melody  Feb 1, 2019