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Sketch |x-a|+a watch

1. How would you sketch this thing????????? i am really confused with sketching modulus functions, I'd appreciate any sort of help !
2. Well, the lowest (or highest, if a is negative) point will be when x = a, so modulus x-a = 0, then it will increase in a x+1 = y+1 way up (or down if a is negative) from that point.
3. (Original post by Kiril)
How would you sketch this thing????????? i am really confused with sketching modulus functions, I'd appreciate any sort of help !
if a is positve

then its a v with the 'point' at (a,a)
(the -a in teh modulus moves it to the right 'a', and the +a moves it up a)
4. Well, we have |k| = k when k >= 0 or |k| = -k when k < 0. Now, we need to sketch y = |x-a| + a so we consider the point at which the sign of (x-a) changes. So we consider the two cases

(1) When x-a >= 0, or x >= a we have |x-a| = x-a. Therefore y = (x-a)+a = x.

(2) When x-a < 0, or x < a we have |x-a| = -(x-a) = a-x. Therefore, y = (a-x)+a = 2a - x

Hence,

y = x for x >= a
y = 2a-x for x < a

which can easily be sketched.

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