1. 4 minutes
Warm-Up
Gina arrived at 9:13am for her 9:30am appointment. She waited for 37 minutes before the nurse called her name. The nurse took Gina’s weight, height, and temperature, which took 4 minutes. After that, she waited another 17 minutes before the doctor came in. At what time did the doctor enter her room?

2. Relations and Functions
Objectives:
To determine whether a given relation is a function
To find the value of a function

3. Relations A relation is a set of ordered pairs.
The domain of a relation is the set of first coordinates.
The range is the set of second coordinates.
{(4,2), (7,2),(-2,8)}
domain: {4,7,-2}
range: {2,8}

4. Functions
A function is a relation that assigns to each member of its domain exactly one member of the range.
The members of the domain can be called inputs and the members of the range can be called outputs.

5. Example 1 Is the following relation a function? Domain Range s t 1 f:t 1 f: u v
Relation f is a function, since each input is matched to only one output.

6. Example 2 Is the following relation a function? Domain Range s t 1 g:t 1 g: u v
Relation g is not a function, since the input s has more than one output.

7. Example 3
Find the domain and range of the relation. Determine if the relation is a function.
h: {(3,6),(-2,3),(1,9),(4,6)}
Domain: {3,-2,1,4}
Range: {6,3,9}
Domain
Range 3 6 -2 3 h: 1 9 4
Relation h is a function, since each input is matched to only one output.

8. Example 4
Find the domain and range of the relation. Determine if the relation is a function.
r: {(5,2),(9,3),(5,4),(6,7)}
Domain: {5,9,6}
Range: {2,3,4,7}
Domain
Range 5 2 9 3 r: 6 4 7
Relation r is not a function, since the input 5 has more than one output.

9. Practice
Find the domain and range of the relation. Determine if the relation is a function.
1) {(6,-6),(7,-7),(3,-3)(4,-4)}
2) {(4,1),(7,1),(-2,4),(1,1)}

10. Example 5 Find the indicated outputs.
f(x) = 3x2; find f(0), f(-1), and f(2).
f(0) =
3(0)2
= 3(0)
= 0
f(-1) =
3(-1)2
= 3(1)
= 3
f(2) =
3(2)2
= 3(4)
= 12

11. Practice Find the indicated outputs.
1) f(x) = x + 3; find f(5), f(-8), and f(-2).
2) g(x) = 3x – x2; find g(0), g(-2), and g(1).
3) p(x) = 2x2 + x - 1; find p(0), p(-2), and p(3).

12. Warm-Up 4 minutes Given that f(x) = 2x2 + 3, find the following:

13. Functions and Graphs Objectives: To recognize a function
To find the domain of a function
To graph a function

14. Graphs of Relations and Functions
Graph the following relations on separate coordinate planes. (on SMART board)
y2 = x + 1
y = x – 1 x y -2 -1 1 2 x y -1 3 8 -3 -2 1
, -1 -1 2
, -2 3
, -3 1

15. Example 1 Is the relation y = 5x a function?
For each input there is only one possible output.
Thus, the relation y = 5x is a function because it assigns exactly one y-value to each x-value.

16. Example 2
Find the domain of the function.

17. Example 3
Find the domain of the function.

18. Practice
Find the domain of each function.
1) f(x) = x2 + 2 2) 3)

19. Example 4
Graph the function f(x) = 2x – 2. State the domain and range.
f(x) = 2x – 2 x y -2 -1 1 2
The domain is all real numbers. -6
The range is all real numbers. -4 -2 2

20. Example 5 Graph the function g(x) = x + 2. State the domain and range.y -2 -1 1 2
The domain is all real numbers. 4
The range is 3 2 3 4

21. Practice Graph each function. State the domain and range.
1) f(x) = x - 1
2) g(x) = -x + 4