Calculus/Precalculus/Exercises

← Graphing linear functions Calculus Hyperbolic logarithm and angles →
Precalculus/Exercises

Algebra edit

Convert to interval notation edit

1.  
 
 
2.  
 
 
3.  
 
 
4.  
 
 
5.  
 
 
6.  
 
 
7.  
 
 
8.  
 
 
9.  
 
 
10.  
 
 

State the following intervals using set notation edit

11.  
 
 
12.  
 
 
13.  
 
 
14.  
 
 
15.  
 
 
16.  
 
 

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.

17.  
false
false
18.  
false
false
19.  
true
true

Evaluate the following expressions edit

20.  
 
 
21.  
 
 
22.  
 
 
23.  
 
 
24.  
 
 
25.  
 
 
26.  
 
 
27.  
 
 
28.  
 
 

Simplify the following edit

29.  
 
 
30.  
 
 
31.  
 
 
32.  
 
 
33.  
 
 
34.  
 
 
35.  
 
 
36.  
 
 

Find the roots of the following polynomials edit

37.  
 
 
38.  
 
 
39.  
 
 
40.  
 
 
41.  
 
 
42.  
 
 
43.  
 
 
44.  
 
 

Factor the following expressions edit

45.  
 
 
46.  
 
 
47.  
 
 

Simplify the following edit

48.  
 
 
49.  
 
 
50.  
 
 
51.  
 
 

Functions edit

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
i.  
 
 
ii.  
 
 
iii.  
 
 
iv.  
 
 
v.  
 
 
vi.  
 
 
vii.  
 
 
viii.  
 
 
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 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).
 
 

Solutions

← Graphing linear functions Calculus Limits →
Precalculus/Exercises