Name:__________________________________________
ALGEBRA Unit Plan – Introduction to Functions
Vocabulary
Function
Example
Relation
Example
Independent
Example
Dependent
Example
Domain
Example
Range
Example
Continuous
Example
Discrete
Example
Scatterplot
Example
Positive Correlation
Example
Negative Correlation
Example
Function Notation
Example
Axes
Example
Intervals
Example
Data Set
Example
OBJECTIVE
A.12 Number and algebraic methods. The student applies the mathematical process standards and algebraic methods
to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to:
(A) decide whether relations represented verbally, tabular, graphically, and symbolically define a function;
(B) evaluate functions, expressed in function notation, given one or more elements in their domains
A.2 Linear functions, equations, and inequalities. The student applies the mathematical process standards when using
properties of linear functions to write and represent in multiple ways, with and without technology, linear equations,
inequalities, and systems of equations. The student is expected to:
(A) determine the domain and range of a linear function in mathematical problems; determine reasonable
domain and range values for real-world situations, both continuous and discrete; and represent domain and
range using inequalities
Essential Questions:
What is a functional relationship?
What is a reasonable domain and range?
How do you identify independent and dependent quantities?
PRE-ASSESSMENT
Pre-requisite skills:
Use inverse operations to set each equation up in y=mx+b form
1. 4x-2y=8
2. -1/2 x+8y=24
3. -2/5 (5x-10)+y=3
Evaluate for the missing variables:
4. Find y when x=4 for y=2x-8
5. Find y when x= -5 for -3x+7=y
6. Find x2 when x=-2
7. Find -x2 when x=-2
8. Find y when x = ½ for 4x2 – 3
9. Find y when x = -1 for -1x2 + 6
10. Find y when x = 1 for -1x2 + 6
SCORE:_______/10
Functions Test Review
Are the following functions? YES or NO. Tell why or why not. Defend your answer.
1.
x
y
-3
6
2
8
5
6
4
24
7
6
2.
3.
_____________________
____________________________
____________________________________
_____________________
____________________________
____________________________________
4.
x
1
3
1
5
y
6
8
-6
13
5. {(0, 0), (2, -4), (2, -2), (3, 6)}
6. {(1, 5) (2, 4) (3, 3) (4, 2)}
_____________________
____________________________
____________________________________
_____________________
____________________________
____________________________________
CONTINUOUS OR DISCRETE?
7..
8.
9.
22
20
18
16
14
12
10
8
6
4
2
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
Discrete or Continuous
Discrete or Continuous
Discrete or Continuous
Domain: ____________________
Domain: ____________________
Domain: ____________________
Range: _____________________
Range: _____________________
Range: _____________________
12.
Domain:______________
13.
Range:_______________
14. Complete the following by circling the appropriate response.
The time/height depends on the time/height.
15. What is the value of f(2)?
16. For f(x)=-3x+14, find f(x) when x=-5
17. For f(x)= 4x2 - 3x + 2, find f(x) when x = -2
18. Define “function” __________________________________________________________________
19. 19. Tony rented a motor scooter on his family vacation to Hawaii. The cost per hour was $25.
a. Which of the following is the dependent variable?
A.
B.
C.
D.
The number of hours he rented the scooter
Any deposit Tony had to pay
The total cost to rent the motorcycle
The hourly rate
b.
b. Describe the independent variable in the situation _____________________________
c.
c. Does this represent a positive, negative or no relationship?_______________________
20. 20. Draw a graph of each of the following types of correlations.
Positive
d.
e.
Negative
No Correlation
21. 21. Use the following situation to draw a graph below:
50
45
40
35
30
25
20
15
10
5
1






2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Amy let her kite reach 45 feet from the ground in 3 minutes.
Amy kept her kite at the same height for 4 minutes.
Amy's kite dropped to 30 feet in 2 minutes.
In 5 minutes, the kite reached 40 feet.
For 5 minutes, Amy kept her height the same.
The wind stopped blowing and Amy’s kite fell to the ground in 1 minute.
21. 22. Describing Graphs Practice: Use the following situation to create a graph below.
My dog, Spot, ran away from home. In 3 hours he traveled 4 miles.
He stopped to get a drink of water and fell asleep for 2 hours.
He woke up and started running 5 miles farther away from home which took him 3 hours.
He got hungry so he decided to head back home. It took him 4 hours to go 7 miles.
It got dark and he couldn’t find his house. He stopped and fell asleep.
28
26
24
22
Distance
20
10
(From
home)
8
6
4
2
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Time (hours)
2
23. Create a table for y=-2x+1 with the domain values of {-3,-1,0,1,3} and graph the function.
y
x
y
x
24. A phone company advertses a new plan in which the customer pays a monthly amount of
$35 for unlimited in the country and $.05 per minute for international calls. Find a function rule for the
monthly payment a customer’s pays according to the new plan. Write the domain and range when a customer uses
30,60,75 and 100 international minutes.
Function rule:____________________________
Domain:________________________________
Range:_________________________________
A
Videos
FUNCTION?
RANGE
Discrete and Continuous
DOMAIN AND