Math 121, Practice Questions Hints And Answers (Page 4 of 5) in pdf

Math 121, Practice Questions Hints And Answers Page 4

10. A charter boat company has determined that the cost, in dollars, of providing x people a

cruise is C(x) = 500 + 50x. The ticket price per person in dollars is 190

(a) Find the revenue function R(x) for providing a tour for x people

Answer: R(x) = x(190

x) =

x + 190x.

R(x) =

x + 190x

(b) Find the proﬁt function P (x) (note: proﬁt is equal to revenue minus cost).

Answer: P (x) = R(x)

C(x) =

x + 190x

(500 + 50x) =

x + 140x

500.

P (x) =

x + 140x

500

the maximum proﬁt).

140

Answer: x =

= 70.

70 tickets

11. Let f (x) =

2x.

(a) Describe in terms of translations how to obtain the graph of g(x) =

2(x + 2)

1 from

the graph of f .

Answer: Shift the graph of f 2 units to the left, and 1 unit down to obtain the graph of g.

(b) Find the formula of a function h whose graph is obtained by translating the graph of f

vertically up two units, and then reﬂecting it over the y-axis.

Answer: h(x) = f ( x) + 2, that is h(x) =

2x + 2.

Math 121, Practice Questions Hints And Answers Page 4