What is the absolute value function?

1 Answer
Scott F.
Mar 24, 2017

#|x-h|=k# means what numbers #x# are #k# away from #h#

Explanation:

Just as a function, #|x|# is the value of #x# without the sign, in other words the distance between #0# and #x#.

For example, #|5|=5# and #|"-"5|=5#.

In an equation, #|x-h|=k# means what numbers #x# are #k# away from #h#.

For example, solving #|x-3|=5# for #x# asks what numbers are 5 away from 3: intuitively the answers are 8 (3+5) and -2 (3-5). Plugging these numbers in for #x# confirms their accuracy.

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