1. 2.1 Notes – Represent Relations and Functions

2. A pairing of input and output values
Relation
Domain
Range
Function
A pairing of input and output values
Input values
(x)
Write from smallest to largest, don’t repeat!
Output values
(y)
Write from smallest to largest, don’t repeat!
Every x value has exactly one y value

3. Domain:_____________ Range: ______________ –3, –1, 3, 5 –3 –4 –4, –2,
1. Identify the domain and range of the given relation. Then represent the relation using a mapping diagram. Is the relation a function? Explain. a. D R
Domain:_____________
Range: ______________
–3,
–1, 3, 5 –3 –4
–4,
–2,
–1, 3 –1 –2
Function YES NO 3 –1
Every x value has exactly one y value 5 3

4. Domain:_____________ Range: ______________ –5, –1, 3, 4 –5 –5 –5, –2,
1. Identify the domain and range of the given relation. Then represent the relation using a mapping diagram. Is the relation a function? Explain. b. D R
Domain:_____________
Range: ______________
–5,
–1, 3, 4 –5 –5
–5,
–2, 4 –1 –2
Function YES NO 3 4
Every x value has exactly one y value 4

5. Domain:_____________ Range: ______________ –4, 4, 5 –4 –2 –2, 1, 2, 5
1. Identify the domain and range of the given relation. Then represent the relation using a mapping diagram. Is the relation a function? Explain. c. D R
Domain:_____________
Range: ______________
–4, 4, 5 –4 –2
–2, 1, 2, 5 4 1
Function YES NO 5 2
4 has two y values 5

6. Domain:_____________ Range: ______________ –2, –1, 0, 1, 2 –2 –4 –4 –1
1. Identify the domain and range of the given relation. Then represent the relation using a mapping diagram. Is the relation a function? Explain. x –2 –1 1 2 y –4 d. D R
Domain:_____________
Range: ______________
–2,
–1, 0, 1, 2 –2 –4 –4 –1
Function YES NO 1
Every x value has exactly one y value 2

7. Domain:_____________ Range: ______________ 1 1 1 1, 2, 4, 7 2
1. Identify the domain and range of the given relation. Then represent the relation using a mapping diagram. Is the relation a function? Explain. e. D R
Domain:_____________
Range: ______________ 1 1 1 1, 2, 4, 7 2
Function YES NO 4
1 has four y values 7

8. Domain:_____________ Range: ______________ –2, –1, 0, 1, 2 –2 1 1, 2,
1. Identify the domain and range of the given relation. Then represent the relation using a mapping diagram. Is the relation a function? Explain. x –2 –1 1 2 y 4 f. D R
Domain:_____________
Range: ______________
–2,
–1, 0, 1, 2 –2 1 1, 2, 4 –1 2
Function YES NO 4 1
Every x value has exactly one y value 2

9. Has two variables with exponents of one.
Function notation
Linear Equation
f(x)
Same thing as “y”
f “at” x NOT f times x!!!!!!
f(5) means x = 5
Has two variables with exponents of one.

10. The values that x can be. The values that y can be.
Domain for equations
Range for equations
The values that x can be.
All x “such that” x is the set of numbers
The values that y can be.
All y “such that” y is the set of numbers

11. once NOT Function Not a Function Vertical Line Test
Given any vertical line, if it crosses the graph _______ it is a function. If it crosses the graph more than once it is ______ a function!
once
NOT
Function
Not a Function

12. a. Linear f(–1) = –4 – 2(–1) = –4 + 2 f(–1) = –2
2. Tell whether the function is linear. Then evaluate the function. a.
Linear
f(–1) =
–4 – 2(–1)
= –4 + 2
f(–1) = –2

13. b. Not Linear g(0) = (0)2 – 1 = 0 – 1 g(0) = –1
2. Tell whether the function is linear. Then evaluate the function. b.
Not Linear
g(0) =
(0)2 – 1
= 0 – 1
g(0) = –1

14. Domain:_____________ Range: ______________
3. Find the domain and range. Then determine if the relation is a function. Explain your reasoning.
Domain:_____________
Range: ______________
Function YES NO
Vertical line test

15. Domain:_____________ Range: ______________
3. Find the domain and range. Then determine if the relation is a function. Explain your reasoning.
Domain:_____________
Range: ______________
Function YES NO
Vertical line test

16. Domain:_____________ Range: ______________
3. Find the domain and range. Then determine if the relation is a function. Explain your reasoning.
Domain:_____________
Range: ______________
Function YES NO
Vertical line test

17. Domain:_____________ Range: ______________
3. Find the domain and range. Then determine if the relation is a function. Explain your reasoning.
Domain:_____________
Range: ______________
Function YES NO
Vertical line test

18. Domain:_____________ Range: ______________
3. Find the domain and range. Then determine if the relation is a function. Explain your reasoning.
Domain:_____________
Range: ______________
Function YES NO
Vertical line test

19. Domain:_____________ Range: ______________
3. Find the domain and range. Then determine if the relation is a function. Explain your reasoning.
Domain:_____________
Range: ______________
Function YES NO
Vertical line test

20. a. D:_____________ R: ______________
4. Graph the function. Then state the domain and range. a.
D:_____________
R: ______________

21. Vertex: (–3, –1) b. –b 2a –(6) 2(1) x = = = –3 y = (–3)2 + 6(–3) + 8
4. Graph the function. Then state the domain and range.
Vertex:
(–3, –1) b. –b 2a
–(6)
2(1)
x = = = –3
y = (–3)2 + 6(–3) + 8
y = –1

22. b. x 4 x 2 (x + 4)(x + 2) = 0 x = –4, –2 D:_____________
4. Graph the function. Then state the domain and range. b. x 4 x 2
(x + 4)(x + 2) = 0
x = –4, –2
D:_____________
R: ______________

23. Vertex: (2, 9) c. –b 2a –(4) 2(-1) x = = = 2 y = –(2)2 + 4(2) + 5
4. Graph the function. Then state the domain and range.
Vertex:
(2, 9) c. –b 2a
–(4)
2(-1)
x = = = 2
y = –(2)2 + 4(2) + 5
y = 9

24. c. x -5 x 1 –(x – 5)(x + 1) = 0 x = 5, –1 D:_____________
4. Graph the function. Then state the domain and range. c. x -5 x 1
–(x – 5)(x + 1) = 0
x = 5, –1
D:_____________
R: ______________

25. Max # of turns: _________ Right End Behavior: _____
4. Graph the function. Then state the domain and range. d.
Max # of turns: _________
Right End Behavior: _____
Left End Behavior: ______
x – intercepts: __________
y – intercepts: __________ 2 ↑ ↓

26. ( )( ) x2
(x + 2)
–1(
x + 2)
(x2 – 1)(x + 2) x 1 x –1
(x + 1)(x – 1)(x + 2) = 0
–1, 1, –2
x – intercepts: _________

27. D:_____________ R: ______________ Max # of turns: _________
Right End Behavior: _____
Left End Behavior: ______
x – intercepts: __________
y – intercept(s): __________ 2 ↑ ↓
D:_____________
R: ______________
–1, 1, –2 –2

28. domain: ____________________
5. State the domain of each function: a.
domain: ____________________

29. domain: ____________________
5. State the domain of each function: b.
domain: ____________________

30. domain: ____________________
5. State the domain of each function: c.
domain: ____________________

31. domain: ____________________
5. State the domain of each function: d.
domain: ____________________