How do the graphs of y = 1/x and y = 5/x+6 compare?

1. State whether the relationship between the variables in the table is a direct variation, an inverse variation, or neither. If it is a direct or inverse variation, write a function to model it.

X: 3, 9, 13, 20

Y: 9, 27, 39, 60

  1. How do the graphs of y = 1/x and y = 5/x+6 compare?

  2. Jane is organizing a fundraiser to buy a ping-pong table for the community center. The table costs $500.00. Jane is asking contributors to pay for an equal share of the cost of the table. she already has five contributors lined up. What function models the cost per share, C, with respect to the number of contributors, n? How many contributors must Jane recruit in order for the cost of each share to be $20.00?

1 Answer

  • 1. Notice that each Y is 3 times the cooresponding x. This means that it is direct variation and the cooresponding function would be

  • f(x) = 3x

    1. 5/x + 6 is stretched vertically and shifted upwards 6 units.

    (if you mean 5/(x+6) then shifted left 6 units instead)

    1. Well if each contributor pays an even cost, then C the cost per share is the same as total cost divided by the number of contributors : C = 500/n.

    It is relatively irrelevant that she already has 5 contributors.

    For the cost per share to be 20 we have

    20 = 500/n So

    n= 500/20 = 50/2 = 25 contributors.

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