Name ________________________________________ Date __________________ Class__________________
LESSON
5-1
Practice B
Variation Functions
Write and graph each function.
1. y varies directly as x, and
y ? 30 when x ? /6.
2. y varies inversely as x, and
y ? 5 when x ? 3.
_________________________________________
________________________________________
Determine whether each data set represents a direction variation, an
inverse variation, or neither.
3.
x
8
12
16
y
2
3
4
4.
_________________________________________
x
3
1
0.5
y
5
15
30
________________________________________
Solve.
5. The number of chaperones, c, needed for the class trip varies directly as
the number of students, s, going on the trip, and c ? 7 when s ? 56. How
many chaperones are needed if 104 students go on the class trip?
_________________________________________________________________________________________
6. The owner of a bookstore developed a model for determining the price of
rare comic books. The price, P, of each book should vary directly with the
number of people, N, that have requested the book and inversely to the
number of such books in existence, M. If N ? 10 people, M ? 10,000 copies,
and P ? $5, then find P for N ? 200 people and M ? 100 copies.
_________________________________________________________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-4
Holt McDougal Algebra 2
Name ________________________________________ Date __________________ Class__________________
LESSON
5-2
Practice B
Multiplying and Dividing Rational Expressions
Simplify. Identify any x-values for which the expression is undefined.
1.
x 2 - 3x - 2
x 2 / 3x / 4
2.
________________________
4.
x 3 - x 2 / 20 x
x 2 / 16
________________________
4x 6
2x 4
3.
_________________________
5.
3 x 2 / 9 x / 12
6x 2 - 9x - 3
__________________________
6.
_________________________
x2 / x3
2x 2 / 5 x - 3
9 / 3x
15 / 2 x / x 2
__________________________
Multiply. Assume all expressions are defined.
7.
4 x - 16 x 2 - 2 x / 3
[
2x - 6
x-4
8.
_________________________________________
x - 3 x 2 / 2x - 1
[
x / 1 x 2 - 5x - 6
________________________________________
Divide. Assume all expressions are defined.
9.
5 x 6 10 x 2
„
y
x2y
10.
_________________________________________
2x 2 / 8 x
x 2 / 2x / 8
„
x 2 / 2 x / 15 2 x 2 / 10 x
________________________________________
Solve. Check your solution.
11.
x 2 - x / 12
? 15
x /3
12.
_________________________________________
2 x 2 - 8 x / 10
?4
2 x 2 - 14 x - 20
________________________________________
Solve.
13. The distance, d, traveled by a car undergoing constant acceleration, a, for a
1
time, t, is given by d ? v 0t - at 2 , where v 0 is the initial velocity of the car.
2
Two cars are side by side with the same initial velocity. One car accelerates,
a ? A, and the other car does not accelerate, a ? 0. Write an expression for
the ratio of the distance traveled by the accelerating car to the distance
traveled by the nonaccelerating car as a function of time.
_________________________________________________________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-12
Holt McDougal Algebra 2
Name ________________________________________ Date __________________ Class__________________
LESSON
5-3
Practice B
Adding and Subtracting Rational Expressions
Find the least common multiple for each pair.
2. x2 - x / 2 and x2 / x / 6
1. 3x2y6 and 5x3y2
_________________________________________
________________________________________
Add or subtract. Identify any x-values for which the expression is
undefined.
3.
2x / 3 4 x / 5
x-4
x-4
4.
_________________________________________
5.
________________________________________
2x
x-4
2
x / x / 12 x / 4
6.
_________________________________________
7.
x - 12 3 x / 2
/
2x / 5 2x / 5
3x 2 / 1
x-2
/
2
x / 3 x / 18 x / 6
________________________________________
x-2
x
x / 2 x / 15 x - 3
8.
2
_________________________________________
2x
x-6
/
x / 7 x / 18 x / 9
2
________________________________________
Simplify. Assume all expressions are defined.
x /1
x
-5
9.
x-6
x /3
12
x
10. 2- 3
x -1
x /2
_________________________________________
________________________________________
Solve.
11. A messenger is required to deliver 10 packages per day. Each day, the
messenger works only for as long as it takes to deliver the daily quota of
10 packages. On average, the messenger is able to deliver 2 packages
per hour on Saturday and 4 packages per hour on Sunday. What is the
messenger’s average delivery rate on the weekend?
_________________________________________________________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-20
Holt McDougal Algebra 2
Name ________________________________________ Date __________________ Class__________________
LESSON
5-4
Practice B
Rational Functions
1
as a guide, describe
x
the transformation and graph the function.
Using the graph of f x 1. g x 2
x4
_________________________________________
Identify the asymptotes, domain, and range of each function.
1
2. g x 5
______________________________________________________
x 3
______________________________________________________
1
1
3. g x ______________________________________________________
x8
______________________________________________________
Identify the zeros and asymptotes of the function. Then graph.
4. f x x 2 4x 5
x 1
a. Zeros:
_________________________________________
b. Vertical asymptote:
_________________________________________
c. Horizontal asymptote:
_________________________________________
d. Graph.
Solve.
5. The number, n, of daily visitors to a new store can be modeled by the function
250 x 1000 , where x is the number of days the store has been open.
n
x
a. What is the asymptote of this function
and what does it represent?
_______________________________________
b. To the nearest integer, how many
visitors can be expected on day 30?
_______________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-28
Holt McDougal Algebra 2