Question 1

Find

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

Find two positive real numbers whose sum is 48 and whose product is a maximum.

Accepted Answer

A) 24 and 24 
B) 44 and 4 
C) 2 and 46 
D) 27 and 21 
E) 31 and 17

Question 3

A cable television firm presently serves 4,600 households and charges $16 per month. A marketing survey indicates that each decrease of $1 in the monthly charge will result in 460 new customers. Let R(x) denote the total monthly revenue when the monthly charge is x dollars. Find the value of x that results in maximum monthly revenue.

Accepted Answer

A) $3 
B) $9 
C) $16 
D) $13 
E) $15

Question 4

Let y = f (x) be a function with domain D = [ -10, -9 ] and range R = [ -10, -7 ]. Find the domain D and range R for the function

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

If the point P (3, 1) is on the graph of a function f, find the corresponding point on the graph of the function

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

Find the distance d (A, B) between the points A (2, - 2) and B (9, 4).

Accepted Answer

A) 9.12 
B) 8.22 
C) 8.92 
D) 9.22 
E) 9.72

Question 7

Find the distance d (A, B) between the points A (4, 2) and B (4, - 5).

Accepted Answer

A) 7 
B) 5 
C) 0 
D) 2

Question 8

Find the domain of

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

If the point P (3, 9) is on the graph of a function f, find the corresponding point on the graph of the function

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

The owner of an ice cream franchise must pay the parent company $1,200 per month plus 7% of the monthly revenue R. Operating cost of the franchise includes a fixed cost of $2,300 per month for items such as utilities and labor. The cost of ice cream and supplies is 53% of the revenue. Determine the monthly revenue needed to break even.

Accepted Answer

A) $5,833 
B) $8,750 
C) $3,500 
D) $1,400 
E) $1,100

Question 11

A 100-foot-long cable of diameter 2 inches is submerged in seawater. Because of corrosion, the surface area of the cable decreases at the rate of 500in 2  per year. Express the diameter d of the cable as a function of time t (in years). (Disregard corrosion at the ends of the cable.)

Accepted Answer

A)   inches 
B)   inches 
C)   inches 
D)   inches 
E)   inches

Question 12

Express the function in the form of  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

Find a composite function form for y if:

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

Find the domain of  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

Find the domain of

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Find the point with coordinates of the form (2a, a) that is in the third quadrant and is a distance 8 from P(2, 1).

Accepted Answer

A) ( - 5.36, - 2.58 ) 
B) ( - 5.26, - 2.63 ) 
C) ( - 5.06, - 2.53 ) 
D) ( - 5.16, - 2.58 ) 
E) ( - 5.36, - 10.71 )

Question 17

Several values of two functions T and S are listed in the following tables: t
0 1 2 3
T(t)
2 3 1 0
X
0 1 2 3
S(x)
1 0 3 2
Find:

Accepted Answer

A)   
B)   
C)   
D)   
E) not possible

Question 18

The owner of an ice cream franchise must pay the parent company $1,100 per month plus 3% of the monthly revenue R. Operating cost of the franchise includes a fixed cost of $2,500 per month for items such as utilities and labor. The cost of ice cream and supplies is 52% of the revenue. Determine the monthly revenue needed to break even.

Accepted Answer

A) $3,600 
B) $8,000 
C) $1,620 
D) $6,545 
E) $1,400

Question 19

An object is projected vertically upward with an initial velocity of  ft/sec, and its distance  in feet above the ground after  seconds is given by the formula  . If the object hits the ground after  seconds, find its initial velocity  in ft/sec.

Accepted Answer

A)   ft/sec 
B)   ft/sec 
C)   ft/sec 
D)   ft/sec 
E)   ft/sec

Question 20

Sketch the graph of f

Accepted Answer

A)   
B)   
C)   
D)

Exam 3: Functions and Graphs

Find

Find two positive real numbers whose sum is 48 and whose product is a maximum.

Let y = f (x) be a function with domain D = [ -10, -9 ] and range R = [ -10, -7 ]. Find the domain D and range R for the function

If the point P (3, 1) is on the graph of a function f, find the corresponding point on the graph of the function

Find the distance d (A, B) between the points A (2, - 2) and B (9, 4) .

Find the distance d (A, B) between the points A (4, 2) and B (4, - 5) .

Find the domain of

If the point P (3, 9) is on the graph of a function f, find the corresponding point on the graph of the function

A 100-foot-long cable of diameter 2 inches is submerged in seawater. Because of corrosion, the surface area of the cable decreases at the rate of 500in² per year. Express the diameter d of the cable as a function of time t (in years) . (Disregard corrosion at the ends of the cable.)

Express the function in the form of .

Find a composite function form for y if:

Find the domain of .

Find the domain of

Find the point with coordinates of the form (2a, a) that is in the third quadrant and is a distance 8 from P(2, 1) .

Several values of two functions T and S are listed in the following tables: t 0 1 2 3 T(t) 2 3 1 0 X 0 1 2 3 S(x) 1 0 3 2 Find:

An object is projected vertically upward with an initial velocity of ft/sec, and its distance in feet above the ground after seconds is given by the formula . If the object hits the ground after seconds, find its initial velocity in ft/sec.

Sketch the graph of f

Exam 3: Functions and Graphs

Find

Find two positive real numbers whose sum is 48 and whose product is a maximum.

Let y = f (x) be a function with domain D = [ -10, -9 ] and range R = [ -10, -7 ]. Find the domain D and range R for the function

If the point P (3, 1) is on the graph of a function f, find the corresponding point on the graph of the function

Find the distance d (A, B) between the points A (2, - 2) and B (9, 4) .

Find the distance d (A, B) between the points A (4, 2) and B (4, - 5) .

Find the domain of

If the point P (3, 9) is on the graph of a function f, find the corresponding point on the graph of the function

A 100-foot-long cable of diameter 2 inches is submerged in seawater. Because of corrosion, the surface area of the cable decreases at the rate of 500in 2 per year. Express the diameter d of the cable as a function of time t (in years) . (Disregard corrosion at the ends of the cable.)

Express the function in the form of .

Find a composite function form for y if:

Find the domain of .

Find the domain of

Find the point with coordinates of the form (2a, a) that is in the third quadrant and is a distance 8 from P(2, 1) .

Several values of two functions T and S are listed in the following tables: t 0 1 2 3 T(t) 2 3 1 0 X 0 1 2 3 S(x) 1 0 3 2 Find:

An object is projected vertically upward with an initial velocity of ft/sec, and its distance in feet above the ground after seconds is given by the formula . If the object hits the ground after seconds, find its initial velocity in ft/sec.

Sketch the graph of f

A 100-foot-long cable of diameter 2 inches is submerged in seawater. Because of corrosion, the surface area of the cable decreases at the rate of 500in² per year. Express the diameter d of the cable as a function of time t (in years) . (Disregard corrosion at the ends of the cable.)