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1. Today:
 Warm Up: (2)
 Khan Academy Topics
 Determining Domain & Range
 Mapping & Verticle Line Test
 Interpreting Graphs
 CW 3.4 Due for Full Credit

2. Warm Up
Make a table of coordinates.
x is the independent variable; we can add our own values of
x. It's best to have at least one negative value, a zero value
and at least one positive value of x.
Substitute each value of x into the equation to get your y value.
You now have the
ordered pairsfor the
graph.
Plot the points and
draw the line.

3. Warm Up
Last one.....

9. Identifying the Domain & Range of a Function
There is no need to list every
point, so the smallest and largest
values are given. (-∞, ∞)
This domain is: (-4, 4)
Notice there are no arrows at the
ends. This is a finite (limited)
value graph.
The range is: (-2, 2)

10. Identifying the Domain & Range of a Function
The domain is:
The range is:
(-2, ∞)
(-∞, ∞)

11. Identifying the Domain & Range of a Function
If y = 5, then; (5)

12. What is a Function?
A function is a relation that assigns each x-value only one y-value.
In order for the relation to be considered a function, each domain
(x) value can be associated with only one range (y) value.
There are two ways to see if a relation is a function:
1. Mappings
2. Vertical Line Test
……….

13. Mapping to Determine a Function
If no graph is available, you can use mapping to determine
whether a relation is a function or not.
Notice that even though there
are two 2’s in the range, you
only list the 2 once.
-1
1
5
6
2
3
8
This relation is a function
because each x-value maps to
only one y-value. It is still a
function if two x-values go to
the same y-value.
Domain Range
{(-1,2) ; (1, 2) ; (5, 3) ; (6, 8)}
Determine whether the following relation is a function:

14. Map the relation to determine whether it is a function
1
5
8
a
b
Is this a function?
Yes
Domain Range

15. Map the relation to determine whether it is a function
{ (1,b), (5, a), (5, c) }
1
5
a
b
c
Domain Range
This is not a function!
The same domain value (5)
has 2 different range values

16. Examples of the Vertical Line Test
Function
Function
Not a function
Not a function
……….
Use the verticle line test when a graph is available

17. Interpreting the Graph
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A. Cost of a laptop, past 10 years B. Drag racing before hitting tree
C. World Population, last 700 years D. Person's height during lifetime
E. Running up, then down a hill F. 3- point shot
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18. Class Work:
CW 3.4;
Due Today

19. The Cost of Renting a Backhoe
y =20x + 50
$50 rental fee plus $20 per hour.
The Process
B. Which one is the independent? The dependent?
Cost, # of hours

20. Functions: A Short Video