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Graphing Absolute Value Functions

This video describes absolute value functions and how they are graphed.

Absolute value functions are similar to regular linear functions, except the absolute value of the bracketed items can never be negative. The absolute value of any number is the measure of its distance from 0, so the graph for an absolute value function will appear shaped like a “V”.

A translation is a shift of a function on the coordinate plane. An absolute value function can be shifted vertically and horizontally.

If a constant is added/subtracted outside of the absolute value bars (ex. |x|+1), the function shifts up or down the amount of units indicated (‘+’ = up, ‘-‘ = down)

If a constant is added/subtracted within the absolute value bars (|x+1|), the function shifts left or right the amount of units indicated. (*** ‘+’ = shift to the LEFT, ‘-‘ shift to the RIGHT***)

An absolute value function can also be dilated or compressed.

If a function is multiplied by a constant larger than one (2|x|), the absolute value function COMPRESSES (narrower).

If a function is multiplied by a constant smaller than one (\frac{1}{2}|x|), the absolute value function STRETCHES (wider).

Graphing can be done through creating a table, and plugging in values to find coordinates.

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