1. Daily Check
Graph the following equations. (2 points each) 1. 2.

2. How do we graph piecewise functions?
Math II
UNIT QUESTION: How are absolute value equations similar to piecewise functions?
Standard: MM2A1
Today’s Question:
How do we graph piecewise functions?
Standard: MM2A1.a,b

3. Piecewise Functions

4. Up to now, we’ve been looking at functions represented by a single equation.
In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain.
These are called piecewise functions.

5. One equation gives the value of f(x) when x ≤ 1
And the other when x>1

6. Evaluate f(x) when x=0, x=2, x=4
First you have to figure out which equation to use
You NEVER use both
X=4
X=2
X=0
This one fits
Into the top
equation
So:
0+2=2
f(0)=2
So:
2(4) + 1 = 9
f(4) = 9
This one fits here
So:
2(2) + 1 = 5
f(2) = 5
This one fits here

7. Graph: For all x’s < 1, use the top graph (to the left of 1)
For all x’s ≥ 1, use the bottom graph (to the
right of 1)

8. x=1 is the breaking
point of the graph.
To the left is the top
equation.
To the right is the
bottom equation.

9. Graph:
Point of Discontinuity

10. Step Functions

12. Graph :

14. Special Step Functions
Two particular kinds of step functions are called ceiling functions ( f (x)= and floor functions ( f (x)= ).
In a ceiling function, all nonintegers are rounded up to the nearest
integer.
An example of a ceiling function is when a phone service company charges by the number of minutes used and always rounds up to the nearest integer of minutes.

15. Special Step Functions
In a floor function, all nonintegers are rounded down to the nearest integer.
The way we usually count our age is an example of a floor function since we round our age down to the nearest year and do not add a year to our age until we have passed our birthday.
The floor function is the same thing as the greatest integer function which can be written as f (x)=[x].

16. Class work
Practice Worksheet

17. Assignment
Practice Worksheet