Calculus/Precalculus/Solutions

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Convert to interval notation[edit]

1.

2.

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9.

This is equivalent to

10.

It helps to draw a picture to determine the set of numbers described:

5 lt x or x lt 6.png

A number in the set can be on either the red or blue line, so the entire number line is included.

State the following intervals using set notation[edit]

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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]

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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 ?

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.

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

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).