4-6 Formalizing Relations and Functions

4-6 Formalizing Relations and Functions Math 8 Plus Mr. Dixon

Vocabulary Relation: a set of ordered pairs (x, y). Domain: the set of x-values. Range: the set of y-values. Vertical Line Test: a method use to determine if a relation of a graph is a function. Function Notation: used to emphasize that the function value f(x) depends on the independent variable x. Other function letters that are used are g and h. Ex: f(x) = - 3x + 1

Ex: #1; Identifying Functions Using Mapping Diagrams Identify the domain and range of the following relation. Represent the relation with a mapping diagram. Is the relation a function? A. {(4.2, 1.5), (5, 2.2), (7, 4.8), (4.2, 0)} Domain: {4.2, 5, 7, 4.2} Domain 4.2

5 7

Range: {1.5, 2.2, 4.8, 0} Range 0 1.5 2.2 4.8

Answer:

Not a Function

Ex: #1; Continued Identify the domain and range of the following relation. Represent the relation with a mapping diagram. Is the relation a function? B. {(6, 5), (4, 3), (5, 8)} Domain: {6, 4, 5}

Range: {5, 3, 8}

Domain 4

5 6

Range 3

Answer:

5 8

Function

Ex: #2; Identifying Functions Using the Vertical Line Test A. Is the relation {(4, 2), (1, 2), (0, 1), (- 2, 2), (3, 3)} a function? Use the vertical line test. Answer: Function

Ex: #2; Continued B. Is the relation a function? Use the vertical line test. y = - x2 + 3

Create a table. X

Y

-2 -1 0 1

-1 2 3 2

2

-1 Answer: Function

Ex: #3; Evaluating a Function The function w(x) = 250x represents the number of words w(x) you can read in x minutes. How many words can you read in 6 min?

w(x) = 250x 1. Substitute

W(6) = 250(6)

2. Simplify

W(6) = 1500

3. Label

1500 words in 6 mins.

Ex: #4; Finding the Range of a Function The domain of g(x) = 4x - 12 is {1, 3, 5, 7}. What is the range? x 1

4x - 12 4(1) - 12

g(x) - 8

3 5 7

4(3) - 12 4(5) - 12 4(7) - 12

0 8 16

The range of g(x) = 4x - 12 is {- 8, 0, 8, 16}

Ex: #5; Identifying a Reasonable Domain and Range You have 7 qt of paint to paint the trim in your house. A quart of paint covers 100 ft2. The function A(q) = 100q represents the area A(q), in square feet, that q quarts of paint cover. What domain and range are reasonable for the function? The least amount of paint I can use is 0 qt. So, that is the least domain value A(0) = 100(0)

A(0) = 0

The greatest amount of paint I can use is 7 qt. So, that is the greatest domain value. A(7) = 100(7)

A(7) = 700

Reasonable Domain: 0 < q < 7

Reasonable Range: 0 < A(q) < 700

Assignment Pgs. 271 – 272 (8 – 22) All Calculators may be used.

Create neat mapping diagrams. Create neat graphs.