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- Find the center and radius of the circle with the following equation:
3 x
2
+ 3 y
2
+ 18 x + 6 y − 60 = 0. 1)
C ( 3 , 1 ), r = 30
C ( 3 , 1 ), r = 30
C (− 3 ,− 1 ), r = 30
C (− 3 ,− 1 ), r = 30
C (9, 3 ), r = 110
C (9, 3 ), r = 110
C (−9,− 3 ), r = 110
C (−9,− 3 ), r = 110
- None of the above
- Hooke’s law states that the force F required to stretch a spring x units beyond its natural length is directly proportional to x. A force of 6 pounds stretches a certain spring from its natural length of 20 inches to a length of 22 inches. Find the force that will stretch the spring from its natural length to 29 inches. 1)
87 pounds
58
3 pounds
29
3 pounds
87 11
pounds
3 pounds
21
11 pounds
12
7 pounds
4
3 pounds
- None of the above
- Solve for x. Find all solutions.
x^3 − 64 = 0
- x^ =^4
- x = − 4
- x = − 4 , 4
- x = − 2 ± 2 3 i
- x = 4 , − 2 ± 2 3 i
- x = − 4 , − 2 ± 2 3 i
- x = − 2 ± 4 3 i
- x = 4 , − 2 ± 4 3 i
- x = − 4 , − 2 ± 4 3 i
- Given
f ( x ) = x^2 − 4 and
g ( x ) = x + 2 , find
( g f )(7).
- None of the above
- Find the domain of the function
f ( x ) =
x
2
− 5 x − 14
(− ∞,−2]∪[7,∞)
[−2,∞)
[−2,7]
[7,∞)
- None of the above
- Solve the inequality. x + 6 + 17 ≥ 25
- (− 14 , 2 )
- [− 14 , 2 ]
- [− 14 ,∞)
- (−∞ ,∞)
- (−∞ ,− 48 ]∪ [2, ∞)
- [ 2 ,∞)
- [− 48 , 2 ]
- (− 48 , 2 )
- None of the above
- Let f ( x ) =
x
. Simplify the difference quotient f ( x + h ) − f ( x ) h , where
h ≠ 0.
h
h^2
3 − 3 h xh^2
- (^) − 3 h^2 x ( x + h )
3 h^2 x ( x + h )
- (^) − 3 h x ( x + h )
3 h x ( x + h )
- −
x ( x + h )
x ( x + h )
- Consider
g ( x ) =
9 x
x + 9
. Find
g ( a ), given that a is a positive real number. Simplify your answer.
9( a − 9 a ) a + 9
3 ( a − 3 a ) a + 9
3 a 2
9( a − 9 a ) a − 81
3 ( a − 3 a ) a − 81
3 a 2
9( a − 9 a ) a − 9
3 ( a − 3 a ) a − 9
3 a^2 + 9 a a − 9
- A music CD sells for $15. The musician receives 10% of the selling price as a royalty for each copy of the CD sold up to 1000 copies. For any additional copies sold beyond 1000, the musician receives 20% of the selling price as a royalty. Find a piece-wise defined function R that gives the total amount of royalties earned by the musician if x copies of the CD are sold.
R ( x ) = 1.5 x if 0 ≤ x ≤ 1000 4.5 x + 1500 if x > 1000
R ( x ) = 1.5 x if 0 ≤ x ≤ 1000 4.5 x if x > 1000
R ( x ) = 1.5 x if 0 ≤ x ≤ 1000 4.5 x − 1500 if x > 1000
R ( x ) = 1.5 x if 0 ≤ x ≤ 1000 4.5 x − 3000 if x > 1000
R ( x ) = 1.5 x if 0 ≤ x ≤ 1000 3 x + 3000 if x > 1000
R ( x ) = 1.5 x if 0 ≤ x ≤ 1000 3 x + 1500 if x > 1000
R ( x ) = 1.5 x if 0 ≤ x ≤ 1000 3 x if x > 1000
R ( x ) = 1.5 x if 0 ≤ x ≤ 1000 3 x − 1500 if x > 1000
R ( x ) = 1.5 x if 0 ≤ x ≤ 1000 3 x − 3000 if x > 1000
- Given the graph of
y = f ( x ) , the graph of
g ( x ) = 2 f ( x ) − 5 can be obtained by using graphical
transformations applied to the graph of f. Which of the following sequences of transformations is correct?
shift right 5 units, then vertical stretch by factor 2
vertical stretch by factor 2, then shift right 5 units
shift down 5 units, then vertical stretch by factor 2
vertical stretch by factor 2, then shift down 5 units
shift right 5 units, then horizontal stretch by factor 2
horizontal stretch by factor 2, then shift right 5 units
shift down 5 units, then horizontal stretch by factor 2
horizontal stretch by factor 2, then shift down 5 units
- None of the above
- Which of the following are true of the function f ( x ) = − 3 x 2 − 6 x − 6? I. A zero of f is – 2. II. f has a y - intercept at
III. The minimum value of f is – 1.
I only
II only
III only
I and II only
I and III only
II and III only
I, II, and III
- Cannot be determined
- None of the above
- A closed rectangular box has a volume of 20 cubic inches. The length of the box is 4 inches. If x denotes the width of the box (in inches) and h denotes the height of the box (in inches), express the surface area of the box, S , as a function of x.
S ( x ) = 40 +
x
+ 8 x
S ( x ) = 10 +
x
+ 8 x
S ( x ) = 10 +
x
+ 4 x
S ( x ) =
x
+ 8 x
S ( x ) = 18 x + 40
S ( x ) = 4 x
2
S ( x ) = 2 x
2
+ 16 x
S ( x ) = 2 x
2
+ 12 x
S ( x ) = 4 x
10 − 4 x
x + 4
h x
- Which of the following are true of the function f ( x ) = x 2 x^2 − 4
I. The range of the function is
(−∞,0]∪ ( 1 ,∞)
II. f has a x - intercept at
III. The graph of f is decreasing on the interval
(− 2 ,0]
I
II
III
I and II
I and III
II and III
I, II, and III
- Cannot be determined
- None of the above
- Find the maximum vertical distance between the graphs of
y 1 = − x
2
+ 4 x and
y 2 = x , when
0 ≤ x ≤ 3.
