Calculus/Precalculus/Solutions

Convert to interval notationEdit

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9.  
This is equivalent to  
 
This is equivalent to  
 
10.  
It helps to draw a picture to determine the set of numbers described:
 

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

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

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 notationEdit

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Which one of the following is a true statement?Edit

17.  
Let  . Then

 , and
 
Thus,  

false
Let  . Then

 , and
 
Thus,  

false
18.  
Using the same example as above, we have  .
false
Using the same example as above, we have  .
false
19.  
true
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  .
 ,  
 ,  
b. What are the domain and range of  ?
The domain is  ; the range is  ,
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,  .
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!
  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.
 . 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.
Yes;   and  . Note that   and its inverse are the same.
54. Does this graph represent a function?  
As pictured, by the Vertical Line test, this graph represents a function.
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?
 
 

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).