I think that this is what you mean
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
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
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.
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.