Name ____________________________________________ Date _____________________ Class ____________________
5.1 Variation Functions
Rational Functions
1.
a. What is the constant of variation for the equation y = 5x ? ____________________
b. Is this a direct or an inverse variation? ____________________
c. If y = 10, what is x ? ____________________
d. If x = 7, what is y ? ____________________
2.
2
a. What is the constant of variation for the equation y = ? ____________________
x
b. Is this a direct or an inverse variation? ____________________
c. If y = 4, what is x ? ____________________
d. If x = 1, what is y ? ____________________
Determine whether each graph represents a direct variation or an indirect variation.
3.
4.
________________________
5.
________________________
________________________
Determine whether each data set represents a direction variation, an inverse variation, or neither.
6.
x
8
12
16
y
2
3
4
____________________________________________
7.
x
3
1
0.5
y
5
15
30
____________________________________________
Write and graph each function.
8. y varies directly as x, and y = 18 when x = 6.
a. What is the constant of variation?
_______________________________
b. Write a direct variation function.
_______________________________
c. Graph the function.
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Holt McDougal Algebra 2
Name ____________________________________________ Date _____________________ Class ____________________
Write and graph each function.
9. y varies directly as x, and y = 30 when x = –6.
____________________________________________
10. y varies inversely as x, and y = 5 when x = 3.
____________________________________________
Solve.
11. The distance, d, Stephan runs each day varies directly with the amount of time, t, that he runs, and d = 10
miles when t = 1.25 h. Find d when t = 1.75 h.
_________________________________________________________________________________________________
12. 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?
_________________________________________________________________________________________________
13. The cost of packing boxes, c, varies inversely with the number of boxes purchased, b, and c = $0.75 when
b = 20. Find c when b = 5.
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14. Joanna’s pay for working overtime, p, varies jointly as the number of hours she works, n, and her hourly
pay rate, r, and p = $103.44 when n = 8 h and r = $8.62. Find n when p = $213.75 and r = $9.50.
_________________________________________________________________________________________________
15. The time, t, required to pick some apples varies directly with the number of bushels of apples to be
picked, b, and inversely to the number of people picking apples, p, and t = 1.5 h when b = 4 and p = 3.
Find b if t = 1.8 h and p = 5.
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16. 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.
Holt McDougal Algebra 2