Calculus/Precalculus/Exercises

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Precalculus/Exercises

Algebra[edit | edit source]

Convert to interval notation[edit | edit source]

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State the following intervals using set notation[edit | edit source]

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

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
false
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false
false
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true
true

Evaluate the following expressions[edit | edit source]

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Simplify the following[edit | edit source]

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Find the roots of the following polynomials[edit | edit source]

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Factor the following expressions[edit | edit source]

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Simplify the following[edit | edit source]

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Functions[edit | edit source]

52. Let .

a. Compute , , and .
, , and
, , and
b. What are the domain and range of  ?
Domain is  ; range is
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 .
No, is not one-to-one. For example, both and result in .

53. Let , .

a. Give formulae for
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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.
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 | edit source]

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