Unit 3: Functions



Unit 3: Functions

Day 2 – Classroom Notes - Functions Basics

I. Old Coordinate Plane Review

[pic][pic] [pic]

II. Definitions: (1) Relation (2) Function:

(2) Domain: (3) Range:

(5) Independent Variable: (6) Dependent Variable:

III. Name 4 ways to display a RELATION.

#1 #2 #3 #4

Example 1) Express the relation as a mapping, graph, and table. {(3,2), (-1,4),(0,-3),(-3,4), (-2,-2)}

[pic] [pic] [pic]

IV. Functions

Ordered Pairs: State whether each set is a function. Answer yes or no. Find the domain and the range.

1) {(2, 5), (5, 6), (2, -6), (3, 8)} Domain: Range:

2) {(1, -2), (8, -4), (-3, 8), (-1, 2)} Domain: Range:

3) {(1, 4), (1, 5), (1, 6), (1, 7)} Domain: Range:

4) {(4, 5), (4, 6), (4, 7), (4, 8)} Domain: Range:

5) {(2, 7), (-5, 3), (1, 6), (-9, 1)} Domain: Range:

Graphs

Use the vertical line test to determine whether each graph is the graph of a function. Answer yes or no.

8) 9) 10) 11)

12) 13)

Function Notation Example:

[pic]

Function Notation: Use [pic] and [pic]to find each value.

14) [pic] 15) [pic] 16) [pic] 17) [pic]

18) [pic] 19) [pic] 20) [pic] 21) [pic]

Functions in Word Problems:

Solve each of the following.

22) The temperature of the atmosphere decreases about 5oF for every 1000 feet increase in altitude. Thus, if the temperature at ground level is 77oF, the temperature t at a given altitude is found by using the equation[pic], where h is the height in feet.

a) Write the equation in function notation.

b) Find f(100), f(200), and f(1000).

23) The table shows the relationship between a and b.

|a |160 |100 |50 |40 |10 |

|b |0.125 |0.2 |0.4 |0.5 |2 |

a) Is the relationship a function? Explain.

b) If the relation can be represented by the equation[pic], rewrite the equation in functional notation so that b is a function of a.

c) What is b when a is 8?

V. Evaluate the indicated function value, and explain the meaning of the point in the context of the problem.

24) The function [pic]models the weight gain of a basketball player as he starts a workout program where g is the weight after x weeks. Evaluate [pic]and explain the meaning.

25) The function [pic]is the function that models the height h of a ball in meters as it is thrown upwards over time t in seconds. Evaluate [pic] and explain the meaning.

26) The function [pic]models the amount of money x in a savings account where x is the standard monthly deposit. Evaluate [pic]and explain the meaning.

VI. HOMEWORK

I. State whether each set is a function. Answer yes or no. Find the domain and the range.

1) {(4, 3), (-2, 10), (5, -6), (10, 7)} Domain: Range:

2) {(-3, -6), (-5, 10), (-1, 2), (0, 0)} Domain: Range:

3) {(2, 7), (3, 7), (5, 7), (6, 7)} Domain: Range:

4) {(7, 2), (7, 3), (7, 4), (7, 5)} Domain: Range:

5) {(2, -6), (3, -5), (-3, 4), (1, 2)} Domain: Range:

6) {(9, 4), (3, 2), (-6, 4), (8, 7)} Domain: Range:

7) {(8, 6), (-5, 2), (0, 6), (-5, 1)} Domain: Range:

II. Use the vertical line test to determine whether each graph is the graph of a function. Answer yes or no.

10) 11) 12) 13)

14) 15) 16) 17)

III. Use [pic] and [pic]to find each value.

18) [pic] 19) [pic] 20) [pic] 21) [pic]

22) [pic] 23) [pic] 24) [pic] 25) [pic]

26) [pic] 27) [pic]

IV. Answer the following questions.

28) What is the origin?

29) Give an example of an ordered pair. The first coordinate is the coordinate and the second coordinate

is the coordinate.

30) What is a relation?

31) What is domain? What is range?

32) What is a function?

33) What is the independent variable? What is the dependent variable?

34) Draw a coordinate axis and label the quadrants.

V. Solve each of the following.

35) Martin earns $7.50 per hour proofreading ads at a local newspaper. His weekly wage w can be described by the equation w = 7.5h, where h is the number of hours worked.

(a) Write the equation in functional notation.

(b) Find w(15), w(20), and w(25).

36) The table shows the relationship between resistance R and current I in a circuit.

|Current (amperes) |0.1 |0.15 |0.25 |2 |3 |

|Resistance (ohms) |120 |80 |48 |6 |4 |

(a) Is the relationship a function? Explain.

(b) If the relation can be represented by the equation IR = 12, rewrite the equation in functional notation so that the resistance R is a function of the current I.

(c) What is the resistance in a circuit when the current is 0.5 ampere?

VI. Evaluate the indicated function value, and explain the meaning of the point in the context of the problem.

37) The function [pic]models the cost of installing carpet in a house where r is the number of rooms in the house and C is the total cost. Evaluate [pic]and explain the meaning.

38) The function [pic] models the height H in meters of a ping pong ball as it is thrown upwards in t seconds. What is the height after 3 seconds.

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