Algebra I Algebraic Connections Algebra II Absolute Value Functions and Graphs

2 Graph: on a Cartesian Plane (two variables: x- axis & y-axis) is V-shaped graph and symmetric about a vertical line called the axis of symmetry. Such a graph has either a single maximum point or a single minimum point, called the VERTEX. See graph on next page. or y = I x I

3 Axis of Symmetry X = 0 (which is the y-axis) Vertex Point (0, 0) (which is the minimum)

4 The Family of Absolute Value Functions: Parent Function: y = |x| y = I x I y = I x I – 3 k = – 3 y = I x I + 2 k = 2 k is the y-coordinate of the vertex point

5 The Family of Absolute Value Functions: Parent Function: y = |x| y = I x I y = I x – 2 I y = I x + 2I h is the x-coordinate of the vertex point (remember the formula has a negative sign in it) y = I x – – 2 I < y = I x – – h I *Form has a subtraction sign! h = – 2 h = 2

6 The Family of Absolute Value Functions: Parent Function: y = |x| y = I x I y = 2 I x I y = ½ I x I Narrow/Skinny Graph Wide/Fat Graph a = the “slope” of the line

7 The Family of Absolute Value Functions: Parent Function: y = |x| y = I x I y = 2 I x + 2 I – 3 y = 2 I x – – 2 I – 3 Vertex (–2, –3) a (slope) = 2 y = ½ I x – 1 I + 1 Vertex (1, 1) a (slope) = ½ Horizontal Translation and Vertical Stretch/Compression: Vertex (h, k) h = – 2 k = – 3

8 The Family of Absolute Value Functions: Parent Function: y = |x| Reflection: In the x-axis: y = – |x| In the y-axis: y = |– x| y = I x I y = – I x I y = I x I or y = I – x I

9 General Form of the Absolute Value Function y = a|x – h| + k The stretch or compression factor is |a| The vertex is located at (h, k) The axis of symmetry is the line x = h. h is the x-coordinate of the vertex point (remember the formula has a negative sign in it) a is the “slope” of the line k is the y-coordinate of the vertex point Translates up or down Translates left or right Stretches/compresses Makes Narrow or Wide k same sign h opposite sign