Calculus/Precalculus/Exercises

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Precalculus/Exercises

Algebra

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Convert to interval notation

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State the following intervals using set notation

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Which one of the following is a true statement?

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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

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Simplify the following

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Find the roots of the following polynomials

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Factor the following expressions

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Simplify the following

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Functions

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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?  
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

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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