September 22, 2011
At the end of today, you will be able to:
Identify and graph linear, squaring functions,
cubic, square root, and reciprocal functions,
and other piecewise-defined functions.
Warm-up:
How much dirt is in a hole that is 2.5
feet wide, 5 feet deep, and 11.2 feet
in length.?
HW 1.6: Pg. 71 #1-3, 29-32 + On “Parent Functions”
Worksheet, Identify the domain and range for each graph.
Correct HW 1.5
1. D: (-∞, -1], [1, ∞), R: [0, ∞)
2. D: (-∞, ∞), R: [0, ∞)
3. D: [-4, 4], R: [0, 4]
4. D: (-∞, 1), (1, ∞), R: [-1, 1]
5. a) 0, b) -1, c) 0, d) -2
9. Function
33. Inc: (-∞, 0) and (2, ∞)
10. Function
Dec: (0, 2)
11. Not a Function
34. Inc: (1, ∞), Dec: (-∞, -1)
12. Not a function.
35. Inc: (-∞, 0) and (2, 0)
15. (-5/2, 0), (6, 0)
Constant: (0, 2)
17. (0, 0)
23. (1/2, 0)
Families of Functions Worksheet
• Go around the room and identify the
parent function given the clues.
• You may have more than one answer!
Lesson 1.6
How do you write a linear function, f for
which f(1) = 3 and f(4) = 0?
Since the function is equal to 3 when x = 1,
you get the point (1, 3)
And the function is equal to 0 when x = 4,
the other point is (4, 0).
*Use two points to find write the equation of
the line using y = mx + b
Step Functions
The Greatest Integer, f(x) = [[x]]
“What is the greatest integer less than…?”
-20
-4
-3
-2
-1
Example 1) Evaluate
a) [[-1]]
b)   1  
 2  
  
= -1
= -1
0
1
2
c)   1  
 10  
  
=0
Example 2) Find h(4.2), if h(x) = [[x + 3]]
h(4.2) = [[4.2 + 3]]
h(4.2) = [[7.2]]
h(4.2) = 7
3
d) [[1.5]]
=1
20
4
What do step functions look like?
f(x) = [[x]]
Make a table and find the points on a graph.
x
y
-1.5
-2
-1
-1
-0.5
-1
0
0
0.5
0
1.5
1
Lesson 1.6
Parent Functions
Parent Functions are the most commonly
used functions in Algebra.
With a pencil, sketch the functions on your
worksheet using your graphing calculator.
You may work with others to complete the
worksheet in 10 minutes.
Linear
f(x) = x
Quadratic
f(x) = x2
Cubic
f(x) = x3
Absolute Value
f(x) = |x|
1
Reciprocal f ( x ) 
x
Square root
f ( x)  x
Greatest Integer
f(x) = [[x]]
f(x) = [|x|]
GAME TIME!
Can you identify the parent function without
looking at your notes?
Write down the function before it disappears!
Good Job! How well did you do?
1. f(x) = √x
2. f(x) = |x|
3. f(x) = x3
1
4. f(x) =
x
5. f(x) = x2
6. f(x) = x
7. f(x) = [[x]]
Graphing Piecewise-Defined
Functions
Example 3)
Sketch the graph of
2 x  3, x  1
f ( x)   2
x , x  1
Make 2 tables for both cases:
x≤1
f(x) = x + 3
x>1
f(x) = x2
1
4
1
1
0
3
2
4
-1
2
3
9
-2
1
4
16
Practice!
2 x  3, x  0
Graph the function f ( x)  
3  x, x  0