Absolute Value Functions

ABSOLUTE VALUE FUNCTIONSGraphsandCompound Functions

ABSOLUTE VALUE FUNCTIONS

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Graphs1. TranslationsQuick GraphsGraphing Inequalities

Writing as Compound Functions4. Using the vertex and slopes5. From Definition

ABSOLUTE VALUE FUNCTIONSTranslations

y =|x|

y = |x+1| + 2

y = |2x+5| - 4

y = 2 |x - 3| + 1

y = 3 |2x - 3| - 4

ABSOLUTE VALUE FUNCTIONSQuick Graphs

y =|x|

y = |x+1| + 2

y = |2x+5| - 4

y = 2 |x - 3| + 1

y = 3 |2x - 3| - 4

ABSOLUTE VALUE FUNCTIONSGraphing Inequalities

y |2x+5| - 4

y > -2 |x - 3| + 1

y |x+1| + 2

y < -2 |3x + 4| + 1

y 3|-2x + 8| - 1

ABSOLUTE VALUE FUNCTIONSWriting asCompound Functionsusing Vertex and slopes

y = | x + 2 | Vertex (-2, 0) Slopes of sidesm = 1right sideleft sideJeff Bivin -- LZHS

y = 3| x - 4 | Vertex (4, 0) Slopes of sidesm = 3right sideleft side

y = -2| x + 1 | VertexSlopes of sidesm = 2right sideleft side

y = 2| x - 5 | +3 Vertex (5, 3) Slopes of sidesm = 2right sideleft side

y = -4| 2x - 5 | + 7 VertexSlopes of sidesm = 8right sideleft side

ABSOLUTE VALUE FUNCTIONSWriting asCompound FunctionsFrom Definition

y = | x + 2 | If x > -2 If x < -2

y = 3| x - 4 | If x > 4 If x < 4

y = -2| x + 1 | If x > -1 If x < -1

y = -3| 2x + 3 | + 1