Graphing Absolute Value Translations of Parent Function 1 /13

Absolute Value y = |x| Remember, everything within the bars comes out as positive. So unless something is being SUBTRACTED from it, or it’s being MULTIPLIED by a Negative, y will ONLY be positive! Y = |x| is known as the Parent Function

Y = |x| Y is positive When x is Positive negative

Absolute Value y = |x| So you notice in the previous graph, there is a single point where the function changes direction – the tip of the V. This point is known as the VERTEX of the function. Many types of functions have vertices (plural or vertex). An absolute value function is largely determined by the position of its vertex. In the Parent Function, it’s just the origin (0,0) -- but it can be moved! Moving the vertex is called “Translation”

Translation Shifting the Parent Function up or down, right or left is known as a TRANSLATION Vertical translation – moving the function up or down. y = |x| + k moves function UP k units y = |x| - k moves function DOWN k units

Y = |x| Y = |x| + 2 Y = |x| - 3

Translation Horizontal Translations -- left or right shift of graph WARNING! THIS ONE IS WEIRD!!!! Left and right translations go the OPPOSITE way from what you would expect. Y = | x – h| goes h units to the RIGHT!!!! Y = |x + h| goes one units to the LEFT. This is always so.

Y = |x| Y = |x - 2| Y = |x + 3|

Translations Of course, you can have both in the same equation. There is a general form to show all possible transformations of the Absolute Value Function.

Work Together p. 221 Lesson Check 1-13