1. Chapter 2 Functions and Linear Functions

2. § 2.1
Introduction to Functions

3. Blitzer, Intermediate Algebra, 4e – Slide #3
Basic Functions
EXAMPLE
Determine whether the following is a function. 1
drums
guitar 2
violin 3
flute 4
Domain
Range
SOLUTION
Yes, because none of the members of the domain correspond to more than one member of the range.
Blitzer, Intermediate Algebra, 4e – Slide #3

4. Blitzer, Intermediate Algebra, 4e – Slide #4
Basic Functions
EXAMPLE
Determine whether the following is a function. 3
ants
beetles 8
crickets 5
moths 9
Domain
Range
SOLUTION
No, because one of the members of the domain, 9, corresponds to more than one member of the range.
Blitzer, Intermediate Algebra, 4e – Slide #4

5. Blitzer, Intermediate Algebra, 4e – Slide #5
Basic Functions
EXAMPLE
Find the indicated function value:
SOLUTION
Replace x with 3
Evaluate the exponent
Multiply
Add and Subtract
Blitzer, Intermediate Algebra, 4e – Slide #5

6. Blitzer, Intermediate Algebra, 4e – Slide #6
Basic Functions
EXAMPLE
Find the indicated function value:
SOLUTION
Replace z with -4
Evaluate the exponents
Multiply
Add
Blitzer, Intermediate Algebra, 4e – Slide #6

7. Blitzer, Intermediate Algebra, 4e – Slide #7
Basic Functions
EXAMPLE
Find the indicated function value:
SOLUTION
Replace w with x+y
Rewrite exponent
Multiply
Add
Distribute
NOTE: THIS CANNOT BE SIMPLIFIED ANY FURTHER!!!
Blitzer, Intermediate Algebra, 4e – Slide #7

8. Blitzer, Intermediate Algebra, 4e – Slide #8
Graphing Functions
EXAMPLE
Graph the function
SOLUTION x
y = -3x+1
Ordered Pair (x,y) -2
f(x) = -3(-2) + 1 = = 7
(-2,7) -1
f(x) = -3(-1) + 1 = = 4
(-1,4)
f(x) = -3(0) + 1 = = 1
(0,1) 1
f(x) = -3(1) + 1 = = -2
(1,-2) 2
f(x) = -3(2) + 1 = = -5
(2,-5)
Blitzer, Intermediate Algebra, 4e – Slide #8

9. Blitzer, Intermediate Algebra, 4e – Slide #9
Graphing Functions
CONTINUED
Blitzer, Intermediate Algebra, 4e – Slide #9

10. Blitzer, Intermediate Algebra, 4e – Slide #10
The Vertical Line Test
EXAMPLE
Use the vertical line test to identify graphs in which y is a function of x.
(a)
(b)
(c)
Blitzer, Intermediate Algebra, 4e – Slide #10

11. Blitzer, Intermediate Algebra, 4e – Slide #11
The Vertical Line Test
CONTINUED
SOLUTION
(a)
(b)
(c)
y is a function of x
y is not a function of x
y is a function of x
Blitzer, Intermediate Algebra, 4e – Slide #11

12. Blitzer, Intermediate Algebra, 4e – Slide #12
Graphs of Functions
EXAMPLE
The figure shows the cost of mailing a first-class letter, f(x), as a function of its weight, x, in ounces. Use the graph to answer the following questions.
Blitzer, Intermediate Algebra, 4e – Slide #12

13. Blitzer, Intermediate Algebra, 4e – Slide #13
Graphs of Functions
CONTINUED
(a) Find f (3). What does this mean in terms of the variables in this situation?
(b) Find f (4). What does this mean in terms of the variables in this situation?
(c) What is the cost of mailing a letter that weighs 1.5 ounces?
(d) What is the cost of mailing a letter that weighs 1.8 ounces?
Blitzer, Intermediate Algebra, 4e – Slide #13

14. Blitzer, Intermediate Algebra, 4e – Slide #14
Graphs of Functions
CONTINUED
SOLUTION
(a) Find f (3). What does this mean in terms of the variables in this situation?
f (3) = This means that when a first-class letter weighs 3 ounces, postage costs 83 cents.
Blitzer, Intermediate Algebra, 4e – Slide #14

15. Blitzer, Intermediate Algebra, 4e – Slide #15
Graphs of Functions
CONTINUED
(b) Find f (4). What does this mean in terms of the variables in this situation?
f (4) = This means that when a first-class letter weighs 4 ounces, postage costs $1.06.
Blitzer, Intermediate Algebra, 4e – Slide #15

16. Blitzer, Intermediate Algebra, 4e – Slide #16
Graphs of Functions
CONTINUED
(c) What is the cost of mailing a letter that weighs 1.5 ounces?
f (1.5) = This means that when a first-class letter weighs 1.5 ounces, postage costs $0.60.
Blitzer, Intermediate Algebra, 4e – Slide #16

17. Blitzer, Intermediate Algebra, 4e – Slide #17
Graphs of Functions
CONTINUED
(d) What is the cost of mailing a letter that weighs 1.8 ounces?
f (1.8) = This means that when a first-class letter weighs 1.8 ounces, postage costs $0.60.
Blitzer, Intermediate Algebra, 4e – Slide #17

18. Obtaining Information from Graphs
Graphs of Functions
Obtaining Information from Graphs
A closed dot indicates that the graph does not extend beyond this point and the point belongs to the graph.
An open dot indicates that the graph does not extend beyond this point and the point does not belong to the graph.
An arrow indicates that the graph extends indefinitely in the direction in which the arrow points.
Blitzer, Intermediate Algebra, 4e – Slide #18

19. Blitzer, Intermediate Algebra, 4e – Slide #19
Domain and Range
EXAMPLE
Use the graph of the function to identify its domain and range.
Blitzer, Intermediate Algebra, 4e – Slide #19

20. Blitzer, Intermediate Algebra, 4e – Slide #20
Domain and Range
SOLUTION
Domain =
{x | x is a real number}
Range =
{y | y }
Blitzer, Intermediate Algebra, 4e – Slide #20