4.6 formalizing relations and functions: domain: the x value of the ordered pair (x, y) relation:...
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4.6 Formalizing Relations and Functions:
Domain: The x value of the ordered pair (x, y)
Relation: the pairing of numbers in one set mainly the domain with exactly one number of the range represented by ordered pairs (x, y)
Range: The y value of the ordered pair (x, y)
Vertical Line Test: If any vertical line passes through a graph more than once it is a relations but not a function.
Function: Only hit the graph once
Not a Function: Hit the graph more than once
Graphs:
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)}
A: {(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)}
Domain(x): {-2, 0, 4, 5}
Range(y):{0.5, 2.5, 6.5}
-2 0 4 5
0.52.56.5
The relation is a FUNCTION since there is only one y for each x.
B: {(6, 5), (4, 3), (6, 4), (5, 8)}
Domain(x):{4, 5, 6}
Range(y):{3, 4, 5, 8}
4 5 6
3 4 5
The relation is a NOT A FUNCTION since the six (x) has two (y) values: 4 and 5.
8
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)}
A: {(4.2, 1.5), (5, 2.2), (7, 4.8), (4.2, 0)}
Domain(x): {4.2, 5, 7}
Range(y):{0, 1.5, 2.2, 4.8}
4.2 5 7
01.52.2
The relation is a NOT A FUNCTION since there is two y’s for 4.2 .
4.8
A: {(-1, 1), (-2, 2), (4, -4), (7, -7)}
Domain(x): {-2, -1, 4, 7}
Range(y):{-7, -4, 1, 2}
-2 -1 4
-7-4 1
The relation is a FUNCTION since there is exactly one y for each x .
2 7
IDENTIFYING FUNCTIONS: A relation is a function if it passes the vertical line test.
1. Decide if the relation is a function.2. Provide domain and Range of the graph
A B C
D E
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
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.
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}
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}
EVALUATION FUNTIONS: We evaluate a function by plugging in a given value of x.
1. Evaluate f(4)
A B
C E A person can type at a speed of w(x) = 250x. How many words will it be in 8 minutes?
EVALUATION FUNTIONS: We evaluate a function by plugging in a given value of x.
1. Evaluate f(4)
Looking at the value of x = 4, we see that the values of y are: - 2, and + 2
Looking at x = 4, we see that the values of y are about: - 1.8, and + 1.8
EVALUATION FUNTIONS: We evaluate a function by plugging in a given value of x.
1. Evaluate f(4)
A person can type at a speed of W(x) = 250x. How many words will it be in 8 minutes?
Looking at the value of x = 4, we see that the value of y will be 64, not in the graph.
We need to replace x for 8.W(x) =250xW(8) = 250(8) W(8) = 2000 words/minute
Y = x3
YOU TRY IT:
Provide the domain and range of the following:
YOU TRY IT (Solution):
Domain: {x | < x < }
RANGE: { y | -2 < y < 2}
CLASSWORK:
Page 271-273
Problems: As many as needed to master the
concept.