# Calculus/Precalculus/Exercises

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< Calculus | Precalculus

## Contents

- 1 Algebra
- 1.1 Convert to interval notation
- 1.2 State the following intervals using set notation
- 1.3 Which one of the following is a true statement?
- 1.4 Evaluate the following expressions
- 1.5 Simplify the following
- 1.6 Find the roots of the following polynomials
- 1.7 Factor the following expressions
- 1.8 Simplify the following

- 2 Functions
- 3 Graphing

## Algebra[edit]

### Convert to interval notation[edit]

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

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

Hint: the true statement is often referred to as the *triangle inequality.* Give examples where the other two are false.

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### Evaluate the following expressions[edit]

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### Simplify the following[edit]

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

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### Factor the following expressions[edit]

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### Simplify the following[edit]

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## Functions[edit]

52. Let .

a. Compute , , and .

b. What are the domain and range of ?

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

53. Let , .

- a. Give formulae for

i.

ii.

iii.

iv.

v.

vi.

vii.

viii.

b. Compute and .

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

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).