1. Formalizing Relations & Functions
After today’s lesson, you should be able to:
Explain the difference between a relation and a function
Identify whether a relation is a function
Identify the domain and range of a relation or a function
Evaluate a function for specified values

2. Are we related?
Determine whether the following quantities are related. Justify your answers
Brother and sister
Step mom and step-son
Distance from work and gas used

3. Relations A ___________is a set of ordered pairs, (x,y).
The (age, height) ordered pairs below form a relation.

4. Domain and Range
The _______ of a relation is the set of the first coordinates of the ordered pairs. The ______ is the set of second coordinates.
List the values in order from least to greatest but ______repeat values!

5. Relations 5 1 10 2 15 3 20 Write the domain. {_______________}
Write the range
How can you tell which is the domain from this mapping? 1 2 3 5 10 15 20

6. Graphing Relations
Write this relation as a set of ordered pairs.
{_________________}
Graph the relation. -2 5 7 -3 6 12

7. Functions
A _________is a relation that assigns exactly one y-value for every x-value.
(x cannot have two different y values!) x y 1 2 3 -6 -1 4 9

8. Functions
Compare and contrast the definition of a relation and a function. Determine if each relation is a function. If not, explain. t
f(t) -5 5 t
f(t) -5 2 7 -1 4

9. Sketch a graph of this function.
Graphing Functions
Sketch a graph of this function. t
f(t) 1 2 3 -6 -1 4 9

10. VERTICAL LINE TEST
If the vertical line passes through more than one point of the graph, the relation ______ a function. Why?
NOT A FUNCTION

11. Mapping Diagram
A mapping diagram draws arrows from the domain of a function to its range.
List the Domain and Range
Domain Range
Is this a function?

12. Exit Ticket
Create a table of at least 4 points Write this relation as a set of ordered pairs Sketch the graph of your relation Is this a function? Justify your answer.

13. Mapping Diagram
Draw a mapping diagram for the following relation? Is it a function?
Domain Range

14. 5-4 & 5-5 Evaluating Functions
To evaluate a function for a specified domain To determine if a rule is that of a function To find the range of a function for a specified domain

15. “Functions Rule” !!
A function rule is an equation that describes a function.
A function rule as an input-output machine.

16. Example: If y = 3x + 4 Another way to write the function y = 3x + 4 is
f(x) = 3x + 4.
x  INPUT f(x)  OUTPUT
This is read as “_______”.
Other notation may be g(x), h(x), etc.

17. Function Junction what’s Your Function!! 

18. Evaluating Functions a) Suppose f(x) = -3x + 10. Evaluate for x = 6
b) Suppose f(x) = -3x Evaluate f(0).
c) Suppose y = -3x + 10.
Evaluate for x = -1

19. Find domain given range
Given y = 3x – 2, what value of x that would make y = 7 What value of x would make y = -17?

20. What’s the range for my domain?
If given the domain, you can find the range of a function.
Example:
Evaluate f(a) = -3a + 5 for the domain
{-3, 1, 4}.
What is the range?

21. What is the output value?
Exit Ticket
The cost of a long distance telephone call, c, is function of the time spent talking. The rule c(t) = 0.09t describes the cost after talking t minutes. What does the domain and range represent in this problem?
Domain -
Range -
Find c(45).
What is the input value?
What is the output value?