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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
avatar+109519 
+4

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
avatar+136 
+2

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
avatar+109519 
+2

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

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