1. More Special Functions
2.6 Day 2 Notes
More Special Functions

2. Step Functions:
a graph consisting of horizontal line segments resembling steps
Graphing Step Functions:
1. Pay attention to whether circles should be open or closed
2. Make horizontal segments at the appropriate y value for the length of the domain for each function.

3. Example 1a: Graph the function.

4. Example 1b: Graph the function.

5. Example 2
Use the graph to find:
f(0)
f(-4)
f(2)
f(-2)
f(1)

6. Absolute Value Functions
Vertex: the corner point of the graph
**Notice that the graph of y = |x| is symmetric in the y-axis
because for every point (x, y) on the graph, the point (-x, y) is also
on the graph.
To the left of x = 0
the graph is
given by the line
y = -x
To the right of x = 0
the graph is given
by the line y = x

7. Graphing absolute value functions
The graph of y = a|x – h| + k has the following
characteristics:
The graph has vertex (h, k) and is symmetric in the line x = h.
The graph is V-shaped. It opens up if a > 0 and down if a < 0.
The right side of the graph has a slope of a.

8. Example 3: b) y = -1/4|x| + 5 a) y = 6|x +3| - 4
i) Tell whether the graph opens up or down.
ii) Find the vertex.
iii) Find the slope of the right side of the graph.
a) y = 6|x +3| - 4
b) y = -1/4|x| + 5

9. Example 4: Graph
a) y = –|x| + 1
b) y = |x – 2| – 3

10. Example 5: