160)
Sketch a graph of f(x) =x3+ 5
160)
161)
Given f(x, y) =x2–yx, find f(u+v, u–v).
161)
Answer:
2uv + 2v2
Explanation:
162)
In June Gail decided to save $20.00 a week. She saved for 14 weeks and then for 14 weeks
she spent $20.00 a week on gifts. Write an absolute–value function to represent the amount
of money Gail had in savings.
162)
Answer:
Explanation:
163)
For the polynomial function f(x) = 4 – 6x–5x3,
Find: (a) the degree, and (b) the leading coefficient
163)
Answer:
Explanation:
164)
Find the domain of the function: f(x) =x– 11
164)
Answer:
Explanation:
Answer:
Explanation:
165)
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.
165)
166)
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?
166)
167)
If h(x) = (2x–3)5, find functions f and g such that h(x) =f(g(x)).
167)
168)
If f(x) =1 – 2x+ 2x, find: (a) f(1) and (b) f(–1).
168)
42
169)
To encourage an even flow of customers, a restaurant varies the price of an item
throughout the day. From 6:00 P.M. to 8:00 P.M. customers pay full price. At lunch from
10:30 A.M. until 2:30 P.M. customers pay half price. From 2:30 until 4:30 customers get a
dollar off the lunch price. From 4:30 P.M. until 6:00 P.M. customers get $5.00 off the dinner
price. From 8:00 until closing time at 10:00 customers get $5.00 off the dinner price. Write a
compound function to represent the cost of an item throughout the day for a dinner price
of d.
169)
170)
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.
170)
171)
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?
171)
172)
List the graphical transformations, in the correct order, that must be done to y=f(x) to
produce the graph of y= 2f(x+ 3) – 5.
172)
173)
Let g(x) =2x+ 3, find g(x+ h) –g(x)
h
173)
174)
The proceeds from an event depend on the number of people who attend.
(a) Write a function p(n) for the proceeds if each ticket costs $8.00 and the number of
tickets sold is n.
(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 p(c), p(c+ 5), and p(c+ 25).
(e) What happens to the proceeds when the number who attend increases by a constant
m? Describe using an equation.
174)
175)
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.
175)
176)
Determine whether the graph of y =0.23 – 0.8x2
0.9 – 0.1x2 is symmetric about the x–axis, the
y–axis, the origin, or the line y=x.
176)
177)
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?
177)
178)
Let g(x) = 1 – 4x, h(x) =x2+ 3x. Find: (a) (g
h)(x); (b) (h
g)(x)
178)
179)
The time it takes to go a given distance depends on the rate.
(a) Write a function t(r) for the time it takes if the distance is 400 miles and the rate is r
miles per hour.
(b) How much time is needed when the rate is x?
(c) If the speed is increased by 10 miles per hour, how much less time is needed?
(d) How much less time is needed per mile per hour increase?
(e) If the speed is increased by h, how much less time is needed?
(f) How much less time is needed per unit increase?
179)
45
180)
Sketch a graph of f(x) =x+ 4 + 7
180)
181)
Determine the x–and y–intercepts, if they exist, of the graph of x2
4–y2
9= 1. Also
determine whether the graph is symmetric about the x–axis, the y–axis, the origin, or the
line y=x.
181)
182)
Sketch a graph of y=2x– 5
182)
183)
The perimeter of a square depends on the length of its side.
(a) Write a function p(l) for the perimeter of a square when the length of its side is l.
(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 p(x), p(2x) and p(3x).
(e) What happens to the perimeter of a square when the side is scaled by a factor s?
Describe using an equation.
183)
184)
Find an equation of the plane that is parallel to the y, z–plane and that passes through the
point (1, 2, 3).
184)
185)
Use a graphing calculator to find all real roots of the equation. Round answers to two
decimal places, if necessary: (x – 1)3= 3 –x2
185)
186)
Sketch the graph of s=f(t) =t+ 2. Also determine the intercepts.
186)
187)
Find the x–intercepts and the y–intercepts of y=x2+ 4x– 5
3
187)
47
188)
The Cobb–Douglas production function for a company is given by P= 20l1/3k2/3 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= 1728 hours and k= $27,000 per month?
188)
189)
If f(x) = 2x +3 and g(x) = 3x– 2, find:
(a) (f
g)(x)
(b) (g
f)(x)
189)
190)
Find: (a) the degree and (b) the leading coefficient of the polynomial function f(x) = 5x+ 7.
190)
191)
A rectangular sheet of metal has a length that is 4 more than the width.
(a) Write the area of the rectangular sheet as a function of the width.
(b) Without simplifying, write the ratio of the length of the sheet to the area of the sheet as
a function of the width.
(c) Simplify the function you wrote in b.
(d) What kind of function is this?
(e) What is its domain out of context?
(f) What is its domain in the given context?
191)
192)
Sketch a graph of f(x) =1
x+ 1
192)
193)
Determine the x– and y–intercepts of the graph of y=x3– 4x.
193)
194)
Determine whether the graph of x=y2– 4 is symmetric about the x–axis, the y–axis, the
origin, or the line y=x.
194)
195)
Find the domain: 3x+ 5
x2+ 5
195)
49
196)
If g(x) =x
x– 4 , find:
(a) the domain
(b) g(0)
(c) g(–4)
(d) g1
2
(e) g(x2)
196)
197)
Given the function F(x) =
2 +x, if x> 3
5, if x= 2
4 –x, if x< 2 ,
find:
(a) the domain
(b) F(2)
(c) F(–2)
(d) F(5)
197)
198)
Find the domain of the function: f(q) =4 – 3q
198)
199)
If f(x) = 5 –x and g(x) =2x2– 3x+ 4, find:
(a) (f +g)(x)
(b) (f–g)(x)
(c) (f – g)(2)
(d) (fg)(x)
(e) (fg)(0)
(f) f
g(x)
(g) f(g(x))
(h) g(f(x))
(i) g(f(1))
199)
200)
Use a graphing calculator to find all real roots of the given function. Round answers to two
decimal places, if necessary: f(x) =x3– 8x – 3
200)
201)
Find the domain of the function: f(x) =x– 1
x2– 9
201)
202)
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.
202)
203)
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
203)
204)
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.
204)
205)
Determine the x– and y–intercepts of the graph of y=7 – 14x
(x+ 2)(x– 1) .
205)
206)
Find the inverse of the function: f(x) =(x –3)2, for x 3
206)
207)
Find the domain of the function: f(x) =x2+x+ 1
207)
208)
If f(x) = 4x2+ 6x, find f(3s).
208)
52
209)
(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.
209)
210)
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.
210)
211)
If f(x) =x2– 2x+ 3, find:
(a) the domain
(b) f(2)
(c) f(–2)
(d) f–1
2
(e) f(t3)
(f) f(s+ 1)
(g) f(x+h)
211)
212)
Find: (a) the degree and (b) the leading coefficient of the polynomial function f(x) = 7 +5x2
–x3.
212)
53
213)
A coffee shop earns $8.75 for every pound of coffee it sells.
(a) Write the profit as a function of the number of pounds of coffee sold.
(b) What kind of function is this?
(c) What is its degree?
(d) What is its leading coefficient?
213)
214)
A coat costs x wholesale. The price the store pays is given by the function s(x) = 1.2x where
x is the wholesale price. The price the customer pays is c(x) = 2x+ 50 where x is the price
the store pays. Write a composite function to find the customer’s price as a function of the
wholesale price.
214)
215)
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.)
215)
216)
If f(x) = 5 – 8x, find:
(a) the domain
(b) f(1)
(c) f(–2)
(d) f5
8
(e) f(t)
(f) f(x+ 2)
216)
217)
The speed you must travel for a given amount of time depends on the distance you must
cover.
(a) Write a function r(d) for the speed if the time is 5 hours and the distance covered is d.
(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 r(x), rx
2 and rx
4,.
(e) What happens to the speed if the distance is reduced (divided) by a constant c?
Describe using an equation.
217)
218)
Find an equation of the plane that is parallel to the x, z–plane and that passes through the
point (–3, 2, 5).
218)
219)
Brett rented a bike from a rental shop and rode at a constant rate of 12 mph for 2.5 hours
along a bike path, and then returned along the same path at the same rate. Write an
absolute–value function to represent Brett’s distance from the rental shop as a function of
time.
219)
220)
Which graphs below represent functions of x?
(a) (b)
(c)
220)
221)
If g(x) =x+ 4 , find g(–5).
221)
222)
A shirt costs x wholesale. The price the store pays is given by the function s(x) =3
2x+ 5,
where x is the wholesale price. The price the customer pays is c(x) = 2(x+ 1) where x is the
price the store pays. Write a composite function to find the customer’s price as a function of
the wholesale price.
222)
223)
Sketch a graph of f(x) =x+ 4
223)
57
224)
Sketch a graph of f(x) =(x– 3)3+ 1
224)
225)
True or False: If x+y2– 5 = 0, then x is a function of y.
225)
226)
In the equation xy2+ 2x +3xy +7y2= 11, is x a function of y?
226)
227)
Determine whether the graph of y2= 4 –x2 is symmetric about the x–axis, the y–axis, the
origin, or the line y=x.
227)
228)
Let f(t) =t2– 1, find (a) f(3t); (b) 3 ×f(t)
228)
229)
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. Write an absolute–value function to represent Julie’s distance from home as she
drove home from the city.
229)
230)
Determine whether the graph y=x2– 1
x is symmetric about the x–axis, the y–axis, the
origin, or the line y=x.
230)
231)
Under certain conditions, if two brown–eyed parents have exactly four children, the
probability P that exactly r of them are blue–eyed is a function of r and is given by P(r) =
4! 1
4
r3
4
4–r
r!(4 –r)! .
Find the probability that exactly thee children will be blue–eyed.
231)
232)
Find an equation of the plane that is parallel to the x, y–plane and that passes through the
point (2, –6, 4).
232)
233)
To reduce inventory, a department store charges three rates. If you buy 0–5 pairs of socks,
the price is $3.50 per pair of socks. If you buy 6–10 pairs of socks, the price is $3.00 per pair.
If you buy more than 10, the price is $2.75 per pair. Graph the compound function that
represents the cost of buying N pairs of socks.
233)
234)
Sketch a graph of f(x) =(x– 4)2
234)
235)
f(x) =.01x2– 3.12 if x 6.3
.39x– 1.2 if x< 6.3
Find: (a) f(6.3); (b) f(0)
235)
236)
Is 3x–2+x–1+ 5 + 6x+11x2 a polynomial function or a rational function? Why?
236)
237)
If f(x) =x+ 4 and g(x) =x3+ 5, find: (a) f(g(x)) and (b) g(f(x)).
237)
60