74)
If g(s) =3
s– 2 –s, find:
(a) the domain
(b) g(0)
(c) g(3)
(d) g(–4)
(e) g1
s
74)
75)
If f(x) =x+ 4 and g(x) =x3+ 5, find: (a) f(g(x)) and (b) g(f(x)).
75)
76)
If g(x) =x2– 2x+ 1, if x < 0
2 – 3x, if x 0 ,
(a) g(–3)
(b) g(0)
(c) g(4)
76)
77)
For the polynomial function f(x) = 4 – 6x–5x3,
Find: (a) the degree, and (b) the leading coefficient
77)
78)
Use the graph of y= f(x).
Sketch a graph of y=f(x+ 3).
78)
79)
(a) Sketch the graph of y= 2x+ 1. (b) Determine the intercepts.
(c) Based on your graph, is y a function of x? If so, state
(d) the domain and (e) the range.
79)
22
80)
Suppose the yearly supply function for paintings from an artist is p= 3000x.
(a) How many paintings per year will be supplied if the price is $21,000 per painting?
(b) How many paintings per year will be supplied if the price is $51,000 per painting?
(c) How does the amount supplied change as the price increases?
80)
81)
In the equation xy2+ 2x +3xy +7y2= 11, is x a function of y?
81)
82)
Find the inverse of the function: f(x) =(x –3)2, for x 3
82)
83)
Bill has charged $2300 on his charge card. He plans to pay $60 a month on his charge cards.
Write an equation to represent the amount he owes excluding any finance charges, and
identify the intercepts.
83)
84)
Find the domain of the function: f(t) =t2–t
4
84)
85)
Traci earns $15.00 per hour and Rich earns $18.00 per hour.
(a) Write a function t(x) for Traci’s earnings as a function of hours worked.
(b) Write a function r(x) for Rich’s earnings as a function of hours worked.
(c) Assuming they work the same number of hours each week, write a function
(t + r)(x) for their combined earnings as a function of hours worked.
85)
23
86)
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))
86)
87)
If h(x) =x2
x2+ 1 , find functions f and g such that h(x) =f(g(x)).
87)
88)
Find the domain of the function: f(x) =x– 1
x2– 9
88)
89)
If f(x) = 3x– 1, find f(x+h) –f(x).
h
89)
24
90)
A cylinder has a height that is 3 times as long as the radius.
(a) Write the area of its circular base as a function of its radius.
(b) Write the volume of the cylinder as a function of its radius.
(c) Without simplifying, write the ratio of the area of the circular base and the volume of
the cylinder as a function of the radius.
(d) Simplify the function you wrote in c.
(e) What kind of function is this?
(f) What is its domain out of context?
(g) What is its domain in the given context?
90)
91)
If f(x) = 3 – 2x and g(x) =x2+ 7, find:
(a) (f
g)(x)
(b) (g
f)(x)
91)
25
92)
Sketch a graph of f(x) =(x– 3)3+ 1
92)
93)
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)
93)
94)
If f(t) = 1.9x2– 3.1x+ 2.01, then find f(x+ 1.1).
94)
26
95)
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)
95)
96)
The weekly salary of an hourly employee depends on the number of hours worked.
Employers are required to pay time and a half if an employee works over 40 hours per
week. Suppose an employer refuses to pay time and a half and time cards are recorded in
half–hour increments.
(a) Write a function s(h) for the weekly salary if a person’s hourly pay is $12.25 and the
number of hours worked is h.
(b) What is the domain of this function out of context?
(c) What is the domain of this function in the given context?
(d) Find s(t), s(t – 5), and s(t– 7).
(e) What happens to the salary if the work time decreases by a constant m? Describe using
an equation.
96)
97)
Which graphs below represent functions of x?
(a) (b)
(c)
97)
98)
Determine whether or not the function is one–to–one: f(x) =7x + 6
98)
99)
Determine whether or not the function is one–to–one: f(x) =(x + 2)3– 8.
99)
28
100)
Sketch a graph of f(x) =(x+ 2)2+ 7
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) = |x| + 4
102)
103)
Determine whether the graph of x=y2– 4 is symmetric about the x–axis, the y–axis, the
origin, or the line y=x.
103)
104)
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?
104)
105)
Determine whether the graph of y=x2–x4 is symmetric about the x–axis, the y–axis, the
origin, or the line y=x.
105)
106)
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. Graph the
absolute–value function to represent the amount Steve has saved since he started buying
holiday gifts over the appropriate domain. (Hint: Let purchases on credit cards represent
negative savings.)
106)
107)
If h(x) =
3x + 4, find functions f and g such that h(x) =f(g(x)).
107)
108)
If g(x) =x
x– 4 , find:
(a) the domain
(b) g(0)
(c) g(–4)
(d) g1
2
(e) g(x2)
108)
109)
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.
109)
111)
Suppose the weekly demand function for a pound of the house blend coffee at a local
coffee shop is p= 15 –q
60 .
(a) If the current price is $11.25 per pound, how much coffee is sold each week?
(b) If they are selling 180 pounds of coffee each week, what is the current price?
(c) If the owner wants to sell 300 pounds of coffee each week, what should the price be?
111)
112)
Julie lives 32 miles from the city. She drove home from the city at a constant rate of 60 mph
along the highway. At the exit 2 miles from her home, she realized she had left her purse at
the department store. She immediately returned to the department store at a rate of 60
mph. Graph the absolute–value function to represent Julie’s distance from home as she
drove home from the city over the appropriate domain.
112)
113)
Given f(x, y) =x2–yx, find f(u+v, u–v).
113)
2uv + 2v2
114)
Find an equation of the plane that is parallel to the x, y–plane and that passes through the
point (2, –6, 4).
114)
110)
110)
115)
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?
115)
116)
Sketch a graph of f(x) =x3+ 5
116)
117)
Suppose a committee of 6 people is to be selected from a group of 25. How many groups
are possible? Represent as a factorial and give the solution.
117)
33
118)
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.
118)
119)
Determine the x– and y–intercepts of the graph of y=x3– 4x.
119)
120)
The graph of y=f(x) is shown below. (a) What is the domain of f? (b) What is the range of
f?
120)
121)
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)
121)
122)
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
122)
123)
For the graph of y =1
x2,
(a) Determine the intercepts.
(b) Determine whether the graph is symmetric about the x–axis,
the y–axis, the origin, or the line y=x.
(c) Sketch the graph. (d) Based on your graph, is y a function of x? If so, state (e)
the domain and (f) the range.
123)
124)
If f(x) =x + 1
x– 7 and g(x) = 2x3, find (f(g(x)).
124)
125)
Determine whether or not the function is one–to–one: f(x) = |x – 8|.
125)
126)
To encourage large group sales, a theater charges two rates. If your group is fewer than 10,
each ticket costs $7.50. If your group is 10 or more, each ticket costs $7.00. Graph the
compound function that represents the cost of buying N tickets.
126)
127)
Determine the x– and y–intercepts of the graph of y=7 – 14x
(x+ 2)(x– 1) .
127)
128)
If g(x) =x + 2
x– 5 , find g(x– 1)
128)
129)
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?
129)
130)
List the graphical transformations, in the correct order, that must be done to y=f(x) to
produce the graph of y= – f(x– 5) + 4.
130)
131)
If h(x) = (2x–3)5, find functions f and g such that h(x) =f(g(x)).
131)
132)
(a) Sketch the graph of y=f(x) = 2x+ 6. (b) Determine the intercepts. State (c) the domain
and (d) the range of f.
132)
36
133)
A daily round trip train ticket to the city costs $4.25. Let x represent the passenger’s income
and y represent the cost of a daily round trip train ticket. Write an equation which
represents the relationship between the cost of a daily round trip ticket and a passenger’s
income; describe the graph of this equation, and identify the intercepts.
133)
134)
Determine whether the graph of y=x– 2x3 is symmetric about the x–axis, the y–axis, the
origin, or the line y=x.
134)
135)
Ellen’s health plan has a $5.00 copayment for complete pregnancy care.
(a) Write the cost of her prenatal care as a function of the number of prenatal visits she
makes.
(b) How does Ellen’s cost change as her number of prenatal visits increases?
(c) What kind of function is this?
135)
136)
If (f(x) = 3 – 2x, find f(f(x)).
136)
137)
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)
137)
138)
Given h(r, s, t, u) =rs
3 –t2, find h(2, 3, 2, 15).
138)
139)
Given the function f(x) =
x2, if –1 <x< 0
2x+ 1, if 0 x< 1,
–x, if 1 x< 2
find:
(a) the domain
(b) f(0)
(c) f(1)
(d) f–1
2
(e) f1
2
(f) f3
2
139)
140)
If f(x) =x2+ 2x– 6, find f(x+h) –f(x).
h
140)
141)
Given the function f(x) =x2+ 4x+ 2, find:
(a) the domain
(b) f(0)
(c) f(3)
(d) f(–2)
(e) f(–t2)
141)
142)
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.
142)
143)
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?
143)
144)
The Parkers are borrowing $120,000 to buy a house. Their monthly payment amount is
given by
P(n, r) =120,000r
1 – (1 +r)–n , where r is the monthly interest rate and n is the number of months.
What is the Parker’s monthly payment if they get:
(a) a 30–year loan at 9% annual interest?
(b) a 20–year loan at 10% annual interest?
144)
145)
Determine the x– and y–intercepts of the graph of y=x4– 16.
145)
146)
In June, Gail decided to save $20.00 a week. She saved for 14 weeks and then for 14 weeks
she spend $20.00 a week on gifts. Graph the absolute–value function to represent the
amount of money Gail had in savings over the appropriate domain.
146)
147)
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?
147)
148)
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?
148)
149)
Find the x–intercepts and the y–intercepts of y=x2+ 4x– 5
3
149)
150)
Determine the x– and y–intercepts, if they exist, of the graph of 9x2+y2+ 8y= 9. Also
determine whether the graph is symmetric about the x–axis, the y–axis, the origin, or the
line y=x.
150)
40