Types of Piecewise functions

1
Types of Piecewise functions

• Step Functions
• functions made up of Horizontal line segments
  with a closed circle on one end and an open
  circle on the other.
• The graph looks like a set of steps
• Absolute Value Functions V-shaped grapg

2
(No Transcript)
3
(No Transcript)
4

• Absolute Value Function- V- Shaped graph.

5
The graph of this piecewise function consists of
2 rays, is V-shaped and opens up.
To the left of x0 the line is y -x
To the right of x 0 the line is y x
6
Write absolute value function as a piecewise
function

•  

•  

7
Graphing Absolute Value functions f(x) a x -
h k

• Vertex is (h,k)
• AOS xh
• If alt 0 the graph opens down (a is negative)
• If agt0 the graph opens up (a is positive)
• The graph is wider if a lt 1 (fraction lt 1)
• The graph is narrower if a gt 1
• a is the slope to the right of the vertex
• (-a is the slope to the left of the vertex)

8
Graph y -x 2 3

1. V (-2,3)
2. Apply the slope a-1 to that point
3. Use the line of symmetry x-2 to plot the 3rd
   point.
4. Complete the graph

9
Graph y -x - 1 1
10
Write the equation for
11

• The vertex is _at_ (0,-3)
• It has the form
• y a x - 0 - 3
• To find a substitute the coordinate of a point
  (2,1) in and solve
• (or count the slope from the vertex to another
  point to the right)
• Remember a is positive if the graph goes up
• a is negative if the graph goes down

So the equation is y 2x -3