# Calculus/Precalculus/Solutions

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< Calculus | Precalculus

## Contents

- 1 Convert to interval notation
- 2 State the following intervals using set notation
- 3 Which one of the following is a true statement?
- 4 Evaluate the following expressions
- 5 Simplify the following
- 6 Find the roots of the following polynomials
- 7 Factor the following expressions
- 8 Simplify the following
- 9 Functions
- 10 Graphing

## Convert to interval notation[edit]

1.

2.

3.

4.

5.

6.

7.

8.

9.

This is equivalent to

10.

## State the following intervals using set notation[edit]

11.

12.

13.

14.

15.

16.

## Which one of the following is a true statement?[edit]

17.

Let . Then

, and

Thus,

**false**

18.

Using the same example as above, we have .

**false**

19.

**true**

## Evaluate the following expressions[edit]

20.

21.

22.

23.

24.

25.

26.

27.

28.

## Simplify the following[edit]

29.

30.

31.

32.

33.

34.

35.

36.

## Find the roots of the following polynomials[edit]

37.

38.

39.

40.

41.

42.

43.

44.

## Factor the following expressions[edit]

45.

46.

47.

## Simplify the following[edit]

48.

49.

50.

51.

## Functions[edit]

52. Let .

a. Compute and .

,

b. What are the domain and range of ?

The domain is ; the range is ,

c. Does have an inverse? If so, find a formula for it.

No, since isn't one-to-one; for example, .

53. Let , .

- a. Give formulae for

i.

.

ii.

.

iii.

.

iv.

.

v.

provided . Note that 0 is not in the domain of , since it's not in the domain of , and you can't divide by something that doesn't exist!

vi.

. Although 0 is still not in the domain, we don't need to state it now, since 0 isn't in the domain of the expression either.

vii.

.

viii.

.

b. Compute and .

; .

c. Do and have inverses? If so, find formulae for them.

Yes; and . Note that and its inverse are the same.

As pictured, by the Vertical Line test, this graph represents a function.

55. Consider the following function

a. What is the domain?

b. What is the range?

c. Where is continuous?

56. Consider the following function

a. What is the domain?

b. What is the range?

c. Where is continuous?

57. Consider the following function

a. What is the domain?

b. What is the range?

c. Where is continuous?

58. Consider the following function

a. What is the domain?

b. What is the range?

c. Where is continuous?

## Graphing[edit]

59. Find the equation of the line that passes through the point (1,-1) and has slope 3.

60. Find the equation of the line that passes through the origin and the point (2,3).