Calculus/Precalculus/Exercises

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Precalculus/Exercises

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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false

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false

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true

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 .

, , and

b. What are the domain and range of  ?

Domain is  ; range is

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

No, is not one-to-one. For example, both and result in .

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.

54. Does this graph represent a function? Sinx over x.svg

Yes.

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).

Solutions

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Precalculus/Exercises