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

Question

Analyze whether the relationship between the variables in the table represents a direct variation, an inverse variation, or neither. If it aligns with either a direct or inverse variation, please provide the corresponding function to model that relationship.

X: 3, 9, 13, 20
Y: 9, 27, 39, 60  
Additionally, compare the graphs of the equations (y = \frac{1}{x}) and (y = \frac{5}{x} + 6). 
Furthermore, Jane is organizing a fundraiser to purchase a ping-pong table for the community center, which costs $500.00. She has already secured five contributors who will each pay an equal share of the table's cost. What function models the cost per share, denoted as (C), in relation to the number of contributors, (n)? Lastly, how many additional contributors must Jane recruit in order for each share to cost $20.00?

Oswaldo Gutmann · Accepted 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

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

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

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.

Anonymous

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

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