1. Find the value of x 2 + 4x + 4 if x = –2.
B. 0
C. 4
D. 16
5–Minute Check 1

2. Evaluate |x – 2y| – |2x – y| – xy if x = –2 and y = 7.
B. 9
C. 19
D. 41
5–Minute Check 3

3. Factor 8xy 2 – 4xy. A. 2x(4xy 2 – y) B. 4xy(2y – 1) C. 4xy(y 2 – 1)
D. 4y 2(2x – 1)
5–Minute Check 4

4. A. B. C. D.
5–Minute Check 5

5. 1.1 Functions
Splash Screen

6. Objectives
Use Set Notation
Use Interval Notation

7. Set – a collection of objects Example: Colors, Cars Element – are the objects that belong to a set. Example: red, orange, blue, …. Nissan, Audi, Jeep, …

8. Infinite Set A set that has an unending list of elements Countable – a collection of objects Uncountable – are the objects that belong to a set.

10. Key Concept 1

11. A. Describe {2, 3, 4, 5, 6, 7} using set-builder notation.
Use Set-Builder Notation
A. Describe {2, 3, 4, 5, 6, 7} using set-builder notation.
The set includes natural numbers greater than or equal to 2 and less than or equal to 7.
This is read as the set of all x such that 2 is less than or equal to x and x is less than or equal to 7 and x is an element of the set of natural numbers.
Example 1

12. B. Describe x > –17 using set-builder notation.
Use Set-Builder Notation
B. Describe x > –17 using set-builder notation.
The set includes all real numbers greater than –17.
Example 1

13. C. Describe all multiples of seven using set-builder notation.
Use Set-Builder Notation
C. Describe all multiples of seven using set-builder notation.
The set includes all integers that are multiples of 7.
Example 1

14. Describe {6, 7, 8, 9, 10, …} using set-builder notation.
Example 1

15. Interval Notation Is a method of writing numbers in a set
Interval Notation Is a method of writing numbers in a set. Recall the Number Line

17. A. Write –2 ≤ x ≤ 12 using interval notation.
Use Interval Notation
A. Write –2 ≤ x ≤ 12 using interval notation.
The set includes all real numbers greater than or equal to –2 and less than or equal to 12.
Answer: [–2, 12]
Example 2

18. B. Write x > –4 using interval notation.
Use Interval Notation
B. Write x > –4 using interval notation.
The set includes all real numbers greater than –4.
Answer: (–4, )
Example 2

19. C. Write x < 3 or x ≥ 54 using interval notation.
Use Interval Notation
C. Write x < 3 or x ≥ 54 using interval notation.
The set includes all real numbers less than 3 and all real numbers greater than or equal to 54.
Answer:
Example 2

20. Write x > 5 or x < –1 using interval notation.B.
C. (–1, 5) D.
Example 2

22. Review Homework

23. 1.1 Functions Continued
What is a function?
How do we use the Vertical Line Test?

24. x represents the domain
y represents the range
Key Concept 3

25. Turn your pencil vertically.
Does you pencil pass through the graph more than once?
Key Concept 3a

26. B. Determine whether the table represents y as a function of x.
Identify Relations that are Functions
B. Determine whether the table represents y as a function of x.
Answer: No; there is more than one y-value for an x-value.
Example 3

27. C. Determine whether the graph represents y as a function of x.
Identify Relations that are Functions
C. Determine whether the graph represents y as a function of x.
Answer: Yes; there is exactly one y-value for each x-value. Any vertical line will intersect the graph at only one point. Therefore, the graph represents y as a function of x.
Example 3

28. Practice WKST

29. Review Homework And Worksheet

30. Extra Help – Second half of Lunch
Quiz on Section 1.1
Tuesday, September 16
Day 4
Extra Help – Second half of Lunch

31. 1.1 – Functions
Objectives
Determine if the equation is a function
Find function values
Find the domain of the function

32. D. Determine whether x = 3y 2 represents y as a function of x.
Identify Relations that are Functions
D. Determine whether x = 3y 2 represents y as a function of x.
To determine whether this equation represents y as a function of x, solve the equation for y.
x = 3y 2 Original equation
Divide each side by 3.
Take the square root of each side.
Example 3

33. Answer: No; there is more than one y-value for an x-value.
Identify Relations that are Functions
This equation does not represent y as a function of x because there will be two corresponding y-values, one positive and one negative, for any x-value greater than 0.
Let x = 12.
Answer: No; there is more than one y-value for an x-value.
Example 3

34. Determine whether 12x 2 + 4y = 8 represents y as a function of x.
A. Yes; there is exactly one y-value for each x-value.
B. No; there is more than one y-value for an x-value.
Example 3

35. To find f (3), replace x with 3 in f (x) = x 2 – 2x – 8.
Find Function Values
A. If f (x) = x 2 – 2x – 8, find f (3).
To find f (3), replace x with 3 in f (x) = x 2 – 2x – 8.
f (x) = x 2 – 2x – 8 Original function
f (3) = 3 2 – 2(3) – 8 Substitute 3 for x.
= 9 – 6 – 8 Simplify.
= –5 Subtract.
Answer: –5
Example 4

36. B. If f (x) = x 2 – 2x – 8, find f (–3d).
Find Function Values
B. If f (x) = x 2 – 2x – 8, find f (–3d).
To find f (–3d), replace x with –3d in f (x) = x 2 – 2x – 8.
f (x) = x 2 – 2x – 8 Original function
f (–3d) = (–3d)2 – 2(–3d) – 8 Substitute –3d for x.
= 9d 2 + 6d – 8 Simplify.
Answer: 9d 2 + 6d – 8
Example 4

37. C. If f (x) = x2 – 2x – 8, find f (2a – 1).
Find Function Values
C. If f (x) = x2 – 2x – 8, find f (2a – 1).
To find f (2a – 1), replace x with 2a – 1 in f (x) = x 2 – 2x – 8.
f (x) = x 2 – 2x – 8 Original function
f (2a – 1) = (2a – 1)2 – 2(2a – 1) – 8 Substitute 2a – 1 for x.
= 4a 2 – 4a + 1 – 4a + 2 – 8 Expand (2a – 1)2 and 2(2a – 1).
= 4a 2 – 8a – 5 Simplify.
Answer: 4a 2 – 8a – 5
Example 4