1. 4.6 Formalizing Relations and Functions:
Relation: the pairing of numbers in one set mainly the domain with exactly one number of the range represented by ordered pairs (x, y)
Domain: The x value of the ordered pair (x, y)
Range: The y value of the ordered pair (x, y)

2. Vertical Line Test: If any vertical line passes through a graph more than once it is a relations but not a function.
Not a Function: Hit the graph more than once
Function: Only hit the graph once

3. Graphs:

4. In math we use a few ways to identify a function:
1. Mapping Diagrams: The use of oval shapes to connect a number of the domain with the number of the range.
EX: Identify the domain and range using a mapping diagram then decide if the relation is a function?
A: {(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)}
B: {(6, 5), (4, 3), (6, 4), (5, 8)}

5. The relation is a FUNCTION since there is only one y for each x.
Domain(x): {-2, 0, 4, 5}
Range(y): {0.5, 2.5, 6.5} -2
0.5
2.5 4
6.5 5
The relation is a FUNCTION since there is only one y for each x.

6. B: {(6, 5), (4, 3), (6, 4), (5, 8)} Domain(x):{4, 5, 6}
Range(y): {3, 4, 5, 8} 3 4 4 5 5 6 8
The relation is a NOT A FUNCTION since the six (x) has two (y) values: 4 and 5.

7. YOU TRY IT:
EX: Identify the domain and range using a mapping then decide if the relation a function?
A: {(4.2, 1.5), (5, 2.2), (7, 4.8), (4.2, 0)}
B: {(-1, 1), (-2, 2), (4, -4), (7, -7)}

8. The relation is a NOT A FUNCTION since there is two y’s for 4.2 .
Domain(x): {4.2, 5, 7}
Range(y): {0, 1.5, 2.2, 4.8}
4.2 5
1.5 7
2.2
4.8
The relation is a NOT A FUNCTION since there is two y’s for 4.2 .

9. The relation is a FUNCTION since there is exactly one y for each x .
Domain(x): {-2, -1, 4, 7}
Range(y): {-7, -4, 1, 2} -2 -7 -1 -4 4 1 7 2
The relation is a FUNCTION since there is exactly one y for each x .

10. IDENTIFYING FUNCTIONS: A relation is a function if it passes the vertical line test.
Decide if the relation is a function.
Provide domain and Range of the graph A B C D E

11. A relation is a function if it passes the vertical line test.
A: Relation that is a function
B: Relation that is Not a function
C: Relation not Function

12. A relation is a function if it passes the vertical line test.
D: Relation that is a function
E: Relation that is Not a function since 3 has two y values.

13. DOMAIN : x values of our graph: RANGE: y values of our graph
D: { x | -∞< x < ∞}
R: { y |0 < y < ∞}
D: { x | 0 < x < ∞}
R: { y | - ∞ < y < ∞}
D: { x | -7 < x < 7}
R: { y |-2 < y < 2}

14. DOMAIN : x values of our graph: RANGE: y values of our graph
D: { x | -∞< x < ∞}
R: { y | - ∞ < y < ∞}
D: { 1, 2, 3}
R: { a, b, c, d}

15. EVALUATION FUNTIONS: We evaluate a function by plugging in a given value of x.
Evaluate f(4) A B
A person can type at a speed of w(x) = 250x. How many words will it be in 8 minutes? E C

16. EVALUATION FUNTIONS: We evaluate a function by plugging in a given value of x.
Evaluate f(4)
Looking at the value of x = 4,
Looking at x = 4,
we see that the values of y are: - 2, and + 2
we see that the values of y are about:
- 1.8, and + 1.8

17. EVALUATION FUNTIONS: We evaluate a function by plugging in a given value of x.
Evaluate f(4)
A person can type at a speed of W(x) = 250x. How many words will it be in 8 minutes?
Y = x3
We need to replace x for 8.
W(x) =250x
W(8) = 250(8)
W(8) = 2000 words/minute
Looking at the value of x = 4,
we see that the value of y will be 64, not in the graph.

18. Provide the domain and range of the following:
YOU TRY IT:
Provide the domain and range of the following:

19. Domain: {x | 𝝅 𝟔 < x < 𝟓𝝅 𝟔 }
YOU TRY IT (Solution):
Domain: {x | 𝝅 𝟔 < x < 𝟓𝝅 𝟔 }
RANGE: { y | -2 < y < 2}

20. CLASSWORK: Page
Problems: As many as needed to master the
concept.