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Math 1111 Quiz 3 Practice Quiz Fall 2007
Name: Last ____________________. First ____________________
You must show your work and/or provide explanations for your answers for all questions.
Otherwise, no credit will be given.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the value for the function.
- Find f(2) when f(x) (^) = x
x + 3
A) 12
B) 6 C) - 4
D) 4
- Find f(x (^) - 1) when f(x) (^) = 5x^2 - 5x (^) - 4. A) 5x^2 - 15x (^) + 6 B) 5x^2 - 25x (^) - 4 C) (^) - 15x^2 + 5x (^) + 6 D) 5x^2 - 15x (^) - 4
Find the domain of the function.
- h(x) = x^ -^4 x3^ - 64x
A) {x|x ≠ 4 } B) {x|x ≠ - 8 , 0, 8 } C) all real numbers D) {x|x ≠ 0}
For the given functions f and g, find the requested function and state its domain.
- f(x) = 5x^3 + 1; g(x) = 5x^2 + 3 Find f · g. A) (f · g)(x) = 25x^6 + 15x^3 + 5x^2 + 3; all real numbers B) (f · g)(x) = 5x^3 + 5x^2 + 3; all real numbers C) (f · g)(x) = 25x^5 + 15x^3 + 5x^2 + 3; {x|x ≠ 0} D) (f · g)(x) = 25x^5 + 15x^3 + 5x^2 + 3; all real numbers
Solve the problem.
- The function f(t) (^) = - 0.13t^2 + 0.53t (^) + 30.1 models the U.S. population in millions, ages 65 and older, where t represents years after 1990. The function g(t) (^) = 0.51t2^ + 12.36t (^) + 105.2 models the total yearly cost of Medicare in billions of dollars, where t represents years after 1990. What does the function g f
represent? Find g f
A) Cost per person in thousands of dollars. $6.09 thousand B) Cost per person in thousands of dollars. $0.20 thousand C) Cost per person in thousands of dollars. $12.64 thousand D) Cost per person in thousands of dollars. $0.16 thousand
- A steel can in the shape of a right circular cylinder must be designed to hold 500 cubic centimeters of juice (see figure). It can be shown that the total surface area of the can (including the ends) is given by S(r) (^) = 2πr2^ + 1000 r
, where r is the radius of the can in centimeters. Using the TABLE
feature of a graphing utility, find the radius that minimizes the surface area (and thus the cost) of the can. Round to the nearest tenth of a centimeter.
A) 5.5 cm B) 0 cm C) 4.3 cm D) 3.5 cm
The graph of a function is given. Decide whether it is even, odd, or neither.
-^ x π - 2 π^ π 2 π
y 5 4 3 2 1
-^ x π - 2 π^ π 2 π
y 5 4 3 2 1
A) even B) odd C) neither
Determine algebraically whether the function is even, odd, or neither.
7x2^ + 8 A) even B) odd C) neither
f(x) = - x^ +^3 if x^ <^2 2x (^) - 3 if x (^) ≥ 2
-5 5 x
y 5
-5 5 x
y 5
A)
-5 5 x
y 5
-5 5 x
y 5
B)
-5 5 x
y 5
-5 5 x
y 5
C)
-5 5 x
y 5
-5 5 x
y 5
D)
-5 5 x
y 5
-5 5 x
y 5
Write an equation that results in the indicated translation.
- The square root function, shifted 7 units to the left A) y (^) = x (^) + 7 B) y (^) = x (^) - 7 C) y (^) = x (^) - 7 D) y (^) = x (^) + 7
Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
- f(x) = |x + 5 | - 7
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
A)
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
B)
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
C)
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
D)
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
Graph the function. State whether it is increasing, decreasing, or constant..
- f(x) = 2x^2 + 20x + 51
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
A) vertex (- 5 , 1 ) intercept (0, 51)
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
B) vertex ( 5 , 1 ) intercept 0,^27 2
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
C) vertex (- 5 , 1 ) intercept 0,^27 2
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
D) vertex ( 5 , 1 ) intercept (0, 51)
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
Determine the quadratic function whose graph is given.
-10 -5 5 10 x
y 10
5
-10 -5 5 10 x
y 10
5
Vertex: (1, 9) y-intercept: (0, 8)
A) f(x) = - x^2 - 4x + 8 B) f(x) = x^2 - 4x + 8 C) f(x) = - x^2 + 2x - 8 D) f(x) = - x^2 + 2x + 8
Solve the problem.
- The manufacturer of a CD player has found that the revenue R (in dollars) is R(p) (^) = - 5p2^ + 1120p, when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar? A) $501,760 B) $62,720 C) $250,880 D) $125,
- A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 240 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? A) 3600 ft^2 B) 7200 ft^2 C) 14,400 ft^2 D) 10,800 ft^2
