1. 8/8/17 Warm Up
Solve the inequality.

2. 8/10/17 Warm Up
Identify the function. 1. 2. 3.

3. Relations & Functions
Domain/Range
Parent Functions

4. A relation is a set of ordered pairs.

5. Domain and Range
The set of input values (x) for a relation is called the domain, and the set of output values (y) is called the range.

6. Function (vertical line test)
a special type of relation in which each element of the domain is paired with exactly one element of the range.

7. Not a function: The relationship from number to letter is not a function because the domain value 2 is mapped to the range values A, B, and C.
Function: The relationship from letter to number is a function because each letter in the domain is mapped to only one number in the range.

8. Families of Functions or Relations

9. Polynomial Functions

10. Constant Functions y = c
Domain:
Range:

11. Identity Function y = x
Domain:
Range:

12. Linear Functions
Domain:
Range:

13. Quadratic Functions y = ax2 + bx + c
Domain:
Range:

14. Cubic Functions
Domain:
Range:

15. Power Functions f(x) = axb
Domain:
Range:

16. Absolute Value Functions y = │x│+1
Domain:
Range:

17. Step Functions and Greatest Integer Function y = [x]
Domain:
Range:

18. Square Root Functions
Domain:
Range:

19. Exponential Functions y = abx y = 3(2)x
Domain:
Range:

20. Logarithmic Functions y = ln x or y = log x
Domain:
Range:

21. Rational Functions or
Domain:
Range:
Domain:
Range:

22. Identify the Function and Find Its Domain and Range

23. Identify the Function and Find Its Domain and Range

24. Trig Functions

25. Sine Function f(x) = sin (x)

26. Cosine Function f(x) = cos (x)

27. Tangent Function f(x) = tan (x)

28. Cotangent Function f(x) = cot (x)

29. Secant Function f(x) = sec (x)

30. Cosecant Function f(x) = csc (x)

31. What do you know about the number system?

32. The Real Number System

33. Name the sets of numbers to which belongs.
The bar over the 9 indicates that those digits repeat forever.
Answer: rationals (Q) and reals (R)
Example 2-1b

34. Name the sets of numbers to which belongs.
lies between 2 and 3 so it is not a whole number.
Answer: irrationals (I) and reals (R)
Example 2-1c

35. Name the sets of numbers to which belongs.
Answer: naturals (N), wholes (W), integers (Z), rationals (Q) and reals (R)
Example 2-1d

36. Name the sets of numbers to which –23.3 belongs.
Answer: rationals (Q) and reals (R)
Example 2-1e

37. Name the sets of numbers to which each number belongs. a.d. e
Answer: rationals (Q) and reals (R)
Answer: rationals (Q) and reals (R)
Answer: irrationals (I) and reals (R)
Answer: naturals (N), wholes (W), integers (Z) rationals (Q) and reals (R)
Answer: rationals (Q) and reals (R)
Example 2-1f

38. Name the sets of numbers to which belongs.
Answer: rationals (Q) and reals (R)
Example 2-1a

39. Properties of Real Numbers

40. Name the property illustrated by .
The Additive Inverse Property says that a number plus its opposite is 0.
Answer: Additive Inverse Property
Example 2-2a

41. Name the property illustrated by .
The Distributive Property says that you multiply each term within the parentheses by the first number.
Answer: Distributive Property
Example 2-2b

42. Name the property illustrated by each equation. a.
Answer: Identity Property of Addition
Answer: Inverse Property of Multiplication
Example 2-2c

43. Identify the additive inverse and multiplicative inverse for –7.
Since –7 + 7 = 0, the additive inverse is 7.
Since the multiplicative inverse is
Answer: The additive inverse is 7, and the multiplicative
inverse is
Example 2-3a

44. Identify the additive inverse and multiplicative inverse for .
Since the additive inverse is
Since the multiplicative inverse is
Answer: The additive inverse is and the multiplicative inverse is 3.
Example 2-3b

45. Answer: additive: –5; multiplicative:
Identify the additive inverse and multiplicative inverse for each number.
a. 5 b.
Answer: additive: –5; multiplicative:
Answer: additive: multiplicative:
Example 2-3c

46. Distributive Property
Simplify
Distributive Property
Multiply.
Commutative Property (+)
Distributive Property
Answer:
Simplify.
Example 2-5a

47. Simplify .
Answer:
Example 2-5b