CHAPTERS 1 & 2 REVIEW

CHAPTERS 1 & 2 REVIEW

January 9, 2012

3. 2(c2 + 4 ) when c = 4

ANSWER 16

ANSWER 40

2. 12 + (5 – 3)2

Evaluate the expression.

ANSWER 15

1. 33 9 + 4 3

SOLUTION

4. Identify the domain and range of the function.

Input 0 1 2 4Output 5 2 2 1

The domain is the set of inputs: 0, 1, 2, and 4

The range is the set of outputs: 1, 2, and 5

24 – (9 + 1)

= 2[9]

5. Evaluate the expression.

a. 7(13 – 8) == 35

Subtract within parentheses.Multiply.

b. 24 – (32 + 1) = Evaluate power.= 24 – 10 Add within parentheses.= 14 Subtract.

c. 2[30 – (8 + 13)] = Add within parentheses.Subtract within brackets.

=18 Multiply.

7(5)

2[30 – 21]

6. Tell whether the pairing is a function. a.

The pairing is not a function because the input 0 is paired with both 2 and 3.

b. OutputInput

21

0 0

4 8

6 12

The pairing is a function because each input is pairedwith exactly one output.

SOLUTION

7. Tell whether the pairing is a function.

1221Output12963Input

36912

1221

The pairing is a function because each input is pairedwith exactly one output.

SOLUTION

8. Tell whether the pairing is a function.

3210Output7422Input

The pairing is not a function because each input is notpaired with exactly one output.

2

47

0123

The range of the function is 0, 4, 10, 14, and 16.

of the function. function, then identify the rangeMake a table for the

2x is 0, 2, 5, 7, and 8. The domain of the function y =

x

y

2 5 70 8

= 2x 2 2 = 4 2 5 =10 2 7 =14 2 8 =162 0 = 0

SOLUTION

9.

10. Write a rule for the function. Input

Output 2

1

6 123

4

8

60 10

SOLUTION

and let y or dependent variable. Notice that eachbe the output,

Let x be the input, or independent variable,

output is 2 more than the corresponding input. So, a rule for the function is y = x + 2.

STEP 1 Make an input-output table.

SOLUTION

Graph the function y = x with domain 0, 2, 4, 6, and 8. 12

x 0 2 4 6 8

y 0 1 2 3 4

11.

STEP 2

Plot a point for each ordered pair (x, y).

Write an equation or an inequality.

12. 3 less than twice a number n is 12.

ANSWER 2n – 3 = 12

13. The product of 5 and a number k is no more than 30.

ANSWER 5k 30 <–

Statement Property illustrated

14. (x + 9) + 2 = x + (9 + 2) Associative property of addition

15. 8.3 + (– 8.3) = 0 Inverse property of addition

16. – y + 0.7 = 0.7 + (– y) Commutative property of addition

Multiplicative property of – 1 Identity property of multiplication

Commutative property ofmultiplication

Associative property of multiplicationMultiplicative property of zero

Property illustratedStatement

x (7 0.5)17. (x 7) 0.5 =

18. 8 0 = 0

19. – 6 y = y (– 6)

20. 9 (– 1) = – 9

21. 1 v =v

8. – 5 (– 6) = – 6 (– 5)

Identify the property illustrated.

Multiplicative property of – 1 Commutative property ofmultiplicationAssociative property of multiplicationMultiplicative property of zeroCommutative property ofmultiplicationMultiplicative property of – 1

22. –1 8 = – 8

12 x = x 1223.

y (4 9) (y 4) 9 =24.

25. 0 (– 41) = 0

27. –13 (– 1) 13=

26.

Different signs; product isnegative.

Same signs; product ispositive.

Multiply 2 and – 5.

Different signs; product isnegative.

Find the product.

28. – 3 (6)

29. 2 (–5) (–4)

= 40

30. – (–4) (–3)12

Multiply – and – 412

= – 6

= – 18

= 2 (– 3)

(–10) (–4)=

Find the product.

31. – 2 (– 7) = (– 2) (– 7)

Same signs; product is positive.= 14

32. – 0.5 (– 4) (– 9) = (2) (– 9) Multiply – 0.5 and – 4.

= – 18 Different signs; product is negative.

Different signs; product isnegative.

33. (–3) (7)43

Multiply and – 3.43

= – 28

= – 4 (7)

Use the distributive property to write an equivalent expression.

34. 4(y + 3) =

35. (y + 7)y =

37. (2 – n)8 =

36. n(n – 9) =

4y + 12

y2 + 7y

n2 – 9n

16 – 8n

= – 15y + 3y2

39. (5 – y)(–3y) =

Simplify.

Simplify.

Distribute – 3y.

= – 2x – 14

Distribute – 2.

Use the distributive property to write an equivalent expression.

38. –2(x + 7) =– 2(x) + – 2(7)

5(–3y) – y(–3y)

Simplify.

= (– 1)(2x) – (–1)(11)

40. –(2x – 11) =of 21Multiplicative property

Distribute – 1.

= – 2x + 11

(–1)(2x – 11)

41. The multiplicative inverse of 15

– is – 5 because

42. The multiplicative inverse of 67

– is 76

– because

15

– (– 5) = 1.

67

– 76

– = 1.

,Order the numbers from least to greatest: 4

3,, – 5 13

–2.5 , 9 .

SOLUTION

Begin by graphing the numbers on a number line.

4 3

ANSWER

Read the numbers from left to right:–2.5, – 5 9 13 . , , ,

43.

Find the product.

44. 7.6 + (–9)

ANSWER –1.4

45. –23.7 + 28.2 + 8.3

ANSWER 12.8

ANSWER Associative property of addition

What property is illustrated by(–y + 3) + 6 = –y + (3 + 6)?

46.

Find the product.

47. –6.5(4)(–2) ANSWER 52

48. 7.4(– 1.2)(3) ANSWER –26.64

ANSWER 12 6x–

Use the distributive property to write an equivalent expression.49. 6(2 x)–

50. x(3x 2)– + ANSWER 3x2 – 2x –

Simplify the expression.51. 4x 5 3 x– + – ANSWER 3x 2–

Find the quotient.

ANSWER 5– 35

ANSWER 316

Simplify the expression

54. 9x 153

––

52. 12

.–.– 14 2

43– .–. (– 4)53.

ANSWER 3x 5+–