MATH 107 UMGC College Algebra Questions

University of Maryland University CollegeMath 107 – College Algebra
Quiz 2
Free Response, Multiple Choice, and Yes/No Problems, 5 Points Each.
You may write answers after problems (you may use Microsoft Equation). If you prefer
handwriting, prepare you answer sheet, scan it, and prepare a file in PDF format.
1. Find the midpoint of the segment with the given endpoints.
8 2
 3 3
 , −  and  − , 
5 9
 4 2
2. Find x- and y-intercepts of the graph of the equation x + 2 y = 4 .
3. Determine if the correspondence is a function
Domain:
a math class
Correspondence:
each person’s IQ
Range:
a set of numbers
Is this correspondence a function?
Yes
4. Given the function p described by p( x) = x3 − x, find p(4)
No
2
5. Determine if the graph is a function.
Yes
No
5
-5
5
-5
For problems # 6-9, find the domain of the function and write it in interval form.
6. f ( x) = 3 +
7. f ( x) =
8
x2
9− x
x2 − 7 x
8. f ( x) = x − 1
9. f ( x) = 3 4 x − 3
10. Determine whether or not (1, 2) is on the graph of y = 14 x − 13 .
Yes
11. Let F ( x) = x 2 − 1 and G( x) = 6 − x , find ( F − G )(9) .
No
3
12 Total profit is defined as total revenue, R(x), minus total cost, C(x), and is given by the
function P(x) = R(x) – C(x). Given R( x) = 60 x − 0.4 x 2 and C ( x) = 2 x + 12 , find each of the
following
a) P(x)=
b) R(80), C(80), and P(80)
h
13. Given that h( x) = x + 4 and g ( x) = x − 7 , find   (7) , if it exists.
g
14. Determine the domain of the quotient of two functions.
f ( x)
f ( x) = 4 x − 9 and g ( x) = 9 x − 36 . Find the domain of
.
g ( x)
A. {x|x is a real number and x  36 }
B. {x|x is a real number and x  −4 }
C. {x|x is a real number and x  4 }
D. {x|x is a real number and x  9 }
15. Find the difference quotient for the function f ( x) = −4 x + 7 and simplify it.
16. Find the domain of the function.
3
g ( x) =
6 − 7x

6
A.  x x is a real number and x  
7

B.  x x is a real number and x  0
C.  x x is a real number and x  3

6
D.  x x is a real number and x  
7

17. Determine the domain and the range of the relation, and tell whether the relation is a
function.
{(9, 9), (24, –7), (37, 9), (9, 5), (48, 5)}
The domain is:….
4
The range is:…
Is this relation a function?
Yes
18. Determine the symmetries (if any) of the graph of the given relation.
y = x2 − 6
A. It is symmetric to the x-axis.
B. It is symmetric to the y-axis.
C. It is symmetric to the origin.
D. It is not symmetric to the x-axis, y-axis, or origin.
19. Determine the symmetries (if any) of the graph of the given relation.
2 x4 + 6 = y 2
Choose the correct symmetries of the graph.
A. x-axis, y-axis, and origin.
B. x-axis only
C. x-axis and y-axis only
D. origin only
20. Find the distance between two points.
(2, –8) and (26, 2)
No
University of Maryland University College
Math 107 – College Algebra
Quiz 2
Free Response, Multiple Choice, and Yes/No Problems, 5 Points Each.
You may write answers after problems (you may use Microsoft Equation). If you prefer
handwriting, prepare you answer sheet, scan it, and prepare a file in PDF format.
1. Find the midpoint of the segment with the given endpoints.
8 2
 3 3
 , −  and  − , 
5 9
 4 2
2. Find x- and y-intercepts of the graph of the equation x + 2 y = 4 .
3. Determine if the correspondence is a function
Domain:
a math class
Correspondence:
each person’s IQ
Range:
a set of numbers
Is this correspondence a function?
Yes
4. Given the function p described by p( x) = x3 − x, find p(4)
No
2
5. Determine if the graph is a function.
Yes
No
5
-5
5
-5
For problems # 6-9, find the domain of the function and write it in interval form.
6. f ( x) = 3 +
7. f ( x) =
8
x2
9− x
x2 − 7 x
8. f ( x) = x − 1
9. f ( x) = 3 4 x − 3
10. Determine whether or not (1, 2) is on the graph of y = 14 x − 13 .
Yes
11. Let F ( x) = x 2 − 1 and G( x) = 6 − x , find ( F − G )(9) .
No
3
12 Total profit is defined as total revenue, R(x), minus total cost, C(x), and is given by the
function P(x) = R(x) – C(x). Given R( x) = 60 x − 0.4 x 2 and C ( x) = 2 x + 12 , find each of the
following
a) P(x)=
b) R(80), C(80), and P(80)
h
13. Given that h( x) = x + 4 and g ( x) = x − 7 , find   (7) , if it exists.
g
14. Determine the domain of the quotient of two functions.
f ( x)
f ( x) = 4 x − 9 and g ( x) = 9 x − 36 . Find the domain of
.
g ( x)
A. {x|x is a real number and x  36 }
B. {x|x is a real number and x  −4 }
C. {x|x is a real number and x  4 }
D. {x|x is a real number and x  9 }
15. Find the difference quotient for the function f ( x) = −4 x + 7 and simplify it.
16. Find the domain of the function.
3
g ( x) =
6 − 7x

6
A.  x x is a real number and x  
7

B.  x x is a real number and x  0
C.  x x is a real number and x  3

6
D.  x x is a real number and x  
7

17. Determine the domain and the range of the relation, and tell whether the relation is a
function.
{(9, 9), (24, –7), (37, 9), (9, 5), (48, 5)}
The domain is:….
4
The range is:…
Is this relation a function?
Yes
18. Determine the symmetries (if any) of the graph of the given relation.
y = x2 − 6
A. It is symmetric to the x-axis.
B. It is symmetric to the y-axis.
C. It is symmetric to the origin.
D. It is not symmetric to the x-axis, y-axis, or origin.
19. Determine the symmetries (if any) of the graph of the given relation.
2 x4 + 6 = y 2
Choose the correct symmetries of the graph.
A. x-axis, y-axis, and origin.
B. x-axis only
C. x-axis and y-axis only
D. origin only
20. Find the distance between two points.
(2, –8) and (26, 2)
No