78)
Determine whether the graph of x2
y2– 9
= 4 is symmetric about the x–axis, the y–axis, the
origin, or the line y=x.
78)
79)
f(x) =x– 2 if x
0
2x+ 1 if x< 0 ; g(x) =x2– 4.
Find:
(a) (f
g)(–1)
(b) (g
f)(–1)
(c) (f
g)(2)
(d) (g
f)(2)
79)
80)
Let f(x) =2x– 3 . Find f(4) –f(–4)
80)
81)
If h(x) =
3x + 4, find functions f and g such that h(x) =f(g(x)).
81)
82)
Suppose the yearly supply function for a particular actor to star in a film is p= 150,000x.
(a) How many films per year is the actor willing to produce if he earns $300,000 per film?
(b) How many films per year is the actor willing to produce if he earns $900,000 per film?
(c) How does the amount supplied change as the price increases?
82)
83)
Find the domain of the function: f(t) =t2–t
4
83)
84)
If f(x) = 3x– 1, find f(x+h) –f(x).
h
84)
21
85)
Determine the x–intercepts and y–intercepts if they exist. Also determine whether the
graph is symmetric about the x–axis, y–axis, the origin, or the line y=x for 3y3=x.
85)
86)
Ellen’s health plan has a $10.00 copayment for complete pregnancy care. Let x represent the
number of prenatal visits and y represent her cost for the pregnancy. Write an equation
which represents the relationship between her cost for the pregnancy and her number of
prenatal visits; describe the graph of this equation, and identify the intercepts.
86)
87)
If f(x) = 1.05x3+ 7.5x2– 1.9, then find f(–0.5)
87)
88)
In November, Steve uses his credit cards to buy $30.00 of holiday gifts each week. After 8
weeks he begins saving $30.00 each week to pay his credit card bill. Write an
absolute–value function to represent the amount Steve has saved since he started buying
holiday gifts. (Hint: Let purchases on credit cards represent negative savings.)
88)
89)
A train holds 200 passengers and departs daily at 8:00 A.M.
(a) Write the daily departure time as a function of the number of people on the train.
(b) How does the departure time change as the number of people on the train increases?
(c) What kind of function is this?
89)
90)
Determine the x– and y–intercepts of the graph of y=x2– 3x– 10
x2+ 2x+ 1
90)
91)
The graph of y=f(x) is shown below. Estimate:
(a) f(–1)
(b) f(0)
(c) f(2)
(d) f(3)
(e) What is the domain of f?
(f) What is the range of f?
91)
92)
If f(x) = 2x + 3 and g(x) =x2– 4x– 2, find:
(a) (f+g)(x)
(b) (f – g)(x)
(c) (fg)(x)
(d) f
g(x)
(e) f(g(x))
(f) g(f(x))
(g) f(g(1))
(h) g(f(1))
92)
23
93)
If h(x) =x2
x2+ 1 , find functions f and g such that h(x) =f(g(x)).
93)
94)
You want to play a lottery that uses 50 numbers. How many combinations are possible if
you need to pick 5 numbers? Represent as a factorial and give the solution.
94)
95)
The area of a circle depends on the length of its radius.
(a) Write a function a(r) for the area of a circle.
(b) How many square units of sod are needed to cover a circular grass area of radius x?
(c) If the radius of the circular grass area is increased by 2 feet, how much more sod is
needed?
(d) How much more sod is needed per foot increase?
(e) If the radius of a circular grass area is increased by h, how much more sod is needed?
(f) How much more sod is needed per unit increase?
95)
96)
The perimeter of a square depends on the length of its side.
(a) Write a function p(l) for the perimeter of a square.
(b) How much linear fencing material is needed to fence a square garden of length x?
(c) If the sides of the square garden are increased by 3 feet, how much more linear fencing
material is needed?
(d) How much more linear fencing material is needed per foot increase?
(e) If the sides of the square garden is increased by h, how much more linear fencing
material is needed?
(f) How much more linear fencing material is needed per unit increase?
96)
97)
If f(x) =
3 –x, if 2 x 5
1 – 2x, if 0 x< 2
7 +x2,if –3 x< 0
,
(a) find the domain of f(x)
(b) find f(3)
97)
98)
Find the inverse of the function: f(x) =8x +3
98)
99)
Let f(x) =x2+ 2x if 0 x
5
3x– 2 if –3 x< 0 ; g(x) = 1 – 4x.
Find:
(a) f(0)
(b) f(–1)
(c) f(4) –f(–2)
(d) f(g(0))
(e) g(f(0))
99)
100)
Find: (a) the degree and (b) the leading coefficient of the polynomial function
P(x) = – x5 + 6x4– 9x2 + 7x + 3
100)
101)
If f(x) =
x2, if x < 0
4x, if 0 x
1
x, if x > 1
, find
(a) f(–2)
(b) f(0)
(c) f1
4
(d) f(1)
(e) f(5)
101)
102)
Sketch a graph of f(x) =1
x– 6 + 4
102)
103)
By looking a the graph below:
(a) list all values for which f(x) = – 2
(b) f(–1) =
(c) f(0) =
(d) domain of f(x) is?
(e) range of f(x) is?
103)
104)
If f(x) = 3 – 2x and g(x) =x2+ 7, find:
(a) (f
g)(x)
(b) (g
f)(x)
104)
105)
Sketch the graph of f(x) =
–1, if x 0
2, if x< 0 , and give the domain and range.
105)
106)
Sketch a graph of f(x) =(x+ 2)2+ 7
106)
27
107)
Given the function f(x) = 3, if x 2
–3, if x< 2, find:
(a) the domain
(b) f(0)
(c) f(2)
(d) f(–2)
(e) f(–3)
107)
108)
The height of an object thrown in the air depends on the time since it’s been thrown. For a
particular situation the height in meters of an object after t seconds can be represented by
h(t) = 20t– 4.9t2.
(a) What is the domain of this function out of context?
(b) What is the domain of this function in the given context?
(c) Find h(s), h(s+ 2), and h(s+ 6).
(d) Use an equation to describe what happens to the height if the time increases by a
constant d.
108)
109)
Tom has saved $1500 for a vacation. He plans to spend $250 a week on his vacation. Write
an equation to represent the amount in savings and identify the intercepts.
109)
110)
Determine whether or not the function is one–to–one: f(x) =x2–3
110)
111)
If f(x) =x + 1
x– 7 and g(x) = 2x3, find (f(g(x)).
111)
28
112)
Given the function f(x) =x2+ 4x+ 2, find:
(a) the domain
(b) f(0)
(c) f(3)
(d) f(–2)
(e) f(–t2)
112)
113)
Suppose the volume of a cube is v(x) = (x–4)3. Express as a composition of two functions
and explain what each function represents.
113)
114)
Determine the x–intercepts if they exist. Also determine whether the graph is symmetric
about the x–axis, y–axis, the origin, or the line y=x for y=x.
114)
115)
The elapsed time in seconds since January 1, 2000 at 12:00 A.M. depends on the elapsed
hours since January 1, 2000 at 12:00 A.M.
(a) Write a function e(h) for the elapsed seconds since January 1, 2000 at 12:00 A.M. when
the elapsed hours are h.
(b) What is the domain of the function out of context?
(c) What is the domain of this function in the given context?
(d) Find e(t), e(–t), e(100t), and e(–100t).
(e) What does multiplying the elapsed hour by –1 mean?
115)
116)
Use a graphing calculator to find all real roots of the given function. Round answers to two
decimal places, if necessary: f(x) =x4–x3–7x2+ 5x + 10 = 0
116)
117)
Sketch a graph of f(x) = |x| + 4
117)
30
118)
Sketch a graph of f(x) = |x+ 3|
118)
119)
Sketch the graph of f(x) =x3+ 1. Also determine the intercepts.
119)
120)
Determine: (a) 5!; (b) 5!
3!2!
120)
121)
In the equation x2+y2= 17; (a) Is x a function of y? (b) Is y a function of x?
121)
31
122)
h(x) =x3– 7x2+ 1; g(x) =x2+ 2x. Find
(a) (h+g)(.1)
(b) (h–g)(.1)
(c) (hg)(.1)
(d) h
g(.1)
122)
123)
Suppose the area of a square tablecloth is t(x) = (x+6)2. Express as a composition of two
functions and explain what each function represents.
123)
124)
If g(x) =x + 2
x– 5 , find g(x– 1)
124)
125)
If g(x) =x2– 2x+ 1, if x < 0
2 – 3x, if x 0 ,
(a) g(–3)
(b) g(0)
(c) g(4)
125)
126)
If f(x) =1
2x+ 3 , then find f(x+h) –f(x)
h and simplify.
126)
127)
Suppose the weekly supply function for a large pizza at a local pizza parlor is p=q
40 .
(a) How many large pizzas will be supplied if the price is $12.50 per pizza?
(b) How many large pizzas will be supplied if the price is $18.75 per pizza?
(c) How does the amount supplied change as the price increases?
127)
128)
Sketch the graph of f(x) =3x + 1, if 0 x< 2
7 – x, if x 2 , and give the domain and range.
128)
129)
A car costs x wholesale. The price the dealer pays is given by the function s(x) =
x+ 500, where x is the wholesale price. The price the customer pays is c(x) =
x+ 1500 where x is the price the dealer pays. Write a composite function to find the
customer’s price as a function of the wholesale price.
129)
130)
If f(x) =x + 1 and g(x) = 3x2 + 4, find f(g(x)).
130)
131)
The Cobb–Douglas production function for a company is given by P= 70l1/4 k3/4 where P
is the monthly production value when k is the amount of the company’s capital investment
(in dollars per month) and l is the size of the labor force (in work hours per month). What
is the production value when l= 2401 hours and k= $10,000 per month?
131)
132)
For the graph of y =f(x) =x2– 4,
(a) Determine the intercepts.
(b) Determine whether the graph is symmetric about the x–axis, y–axis, the origin, or the
line y=x.
(c) Sketch the graph. State (d) the domain and (e) the range of f.
132)
133)
By looking a the graph below:
(a) list all values for which f(x) = 0
(b) f(2) =
(c) f(–2) =
(d) domain of f is?
(e) range of f is?
133)
134)
If f(x) =x2 and g(x) = 2x+ 1, find:
(a) (f + g)(x)
(b) (f + g)(3)
(c) (f – g)(x)
(d) (fg)(x)
(e) (fg)–1
2
(f) f
g (t2)
(g) f(g(x))
(h) f(g(1))
(i) g(f(x))
134)
135)
Suppose an artist always paints rectangular pictures using a square of unknown length as
a reference. She always makes the length 4 units longer than the square, and the width is 2
units longer than the square.
(a) Write a function l(x) for the length of a painting as a function of the length of the
square.
(b) Write a function a(x) for the area of a painting as a function of the length of the square.
(c) Write a function l
a(x) for the ratio of the length to the area as a function of the length
of the square.
135)
136)
If f(x) = 7, find f(14).
136)
137)
Determine whether the graph of y=x2–x4 is symmetric about the x–axis, the y–axis, the
origin, or the line y=x.
137)
138)
The train holds 175 passengers. It departs daily at 9:00 A.M. Let x represent the time and y
represent the number of passengers. Write an equation which represents the relationship
between the number of passengers on the train and the train’s departure time. Describe the
graph of this equation, and identify the intercepts.
138)
139)
Let h(x) =7 –x. Find functions f and g such that h=f
g.
139)
140)
Determine whether the graph of y2=7 – 9x2
1
x2– 1
is symmetric about the x–axis, the y–axis, the
origin, or the line y=x.
140)
141)
Sketch the surface x+y= 3.
141)
142)
Suppose the yearly demand function for an artist’s paintings is p=25,000
q.
(a) If the current prices is $200.00 per painting, how many paintings are sold each year?
(b) If the artist wants to sell 4 paintings per year, what should the price be?
142)
143)
The graph of y=f(x) is shown below. (a) What is the domain of f? (b) What is the range of
f?
143)
144)
Determine whether or not the graph of y=x2 (x2– 9)
x4+ 4 is symmetric about the x–axis, the
y–axis, the origin, or the line y=x.
144)
145)
Find the domain of the function f(x) = 6.
145)
146)
If g(x) =
x2– 1, if –1 x
2
2x – 3, if –3 x< – 1
x2+ 1, if –5 x< – 3
(a) find the domain of f(x)
(b) find f(2) +f(–2)
146)
147)
Determine whether or not the function is one–to–one: f(x) =7x + 6
147)
148)
Suppose f(x) =xy2+ 3xy –y2. Find f(y).
148)
37
149)
(a) Sketch the graph of y=f(x) = 2x+ 6. (b) Determine the intercepts. State (c) the domain
and (d) the range of f.
149)
150)
The height of an object thrown in the air depends on the time since it has been thrown. For
a particular situation the height in meters of an object after t seconds can be represented by
h(t) = 32t– 4.9t2.
(a) What kind of function is this?
(b) What is its degree?
(c) What is its leading coefficient?
150)
151)
Find the domain of the function: F(x) =2x+ 3
151)
152)
The response R to a shock of intensity I is a number estimated by R=f(I) =I2
1000 .
(a) Express f(2I0) in terms of f(I0).
(b) What effect does the doubling of intensity have on response?
152)
153)
Sketch the graph of f(x) =x2– 2x. Also determine the intercepts.
153)
154)
If g(s) =3
s– 2 –s, find:
(a) the domain
(b) g(0)
(c) g(3)
(d) g(–4)
(e) g1
s
154)
155)
To encourage conservation, a gas company charges two rates. You pay $0.53 per therm for
0–70 therms and $0.74 for each therm over 70. Write a compound fraction to represent the
monthly cost of t therms of water.
155)
156)
Let p= 500 –1
2q represent a demand equation for a product where p is unit price and q is
quantity with the restriction 0 q< 1000. Express the quantity q as a function of p.
156)
157)
Sketch a graph of f(x) =(x– 5)3
157)
158)
Given the function f(x) =
2x, if 0 <x< 1
1 –x, if 1 x< 2,
0, if 2 x
3
find:
(a) the domain
(b) f(1)
(c) f(2)
(d) f(3)
(e) f(0.1)
158)
159)
If f(x) =x2+ 2x– 6, find f(x+h) –f(x).
h
159)
40