Calculus/Precalculus/Exercises

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Precalculus/Exercises

Contents

AlgebraEdit

Convert to interval notationEdit

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State the following intervals using set notationEdit

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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 expressionsEdit

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Simplify the followingEdit

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Find the roots of the following polynomialsEdit

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Factor the following expressionsEdit

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Simplify the followingEdit

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FunctionsEdit

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
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ii.

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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?

GraphingEdit

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