2. Absolute Value Functions
• The absolute value of x is defined by:
• The graph of y = |x| looks like a v-shape.
vertex
3. Why are they important?
• Have you ever played pool or putt-putt
golf?
• The path of the ball when making a bank
shot is an example of an absolute value
function.
4. Transformations
• There are four ways the absolute value graph
can be changed:
1. Open Up or Open Down
2. Change in Width – sides can be steeper or
less steep
3. Horizontal Shift – vertex moves left or right
4. Vertical Shift- vertex moves up or down
5. General Form
• y = a |x – h| + k
• Effects of a:
• When a > 0 (positive), the V opens up.
• When a < 0 (negative), the V opens down.
• When |a| < 1, the sides are less steep than
y = |x|.
• When |a| > 1, the sides are steeper than
y = |x|.
11. Graphing Absolute Value Functions
• Plot the vertex.
• Sketch the axis of symmetry.
• Use a (the slope) to graph the right side.
• Use symmetry to draw in the left side.
• Example:
Graph