1. does the table below represent direct variation, inverse variation, or neither? how do you know? if it is a direct or inverse variation, write a function to model it.
x 3 4 7 10
y 12 16 28 40
2. how do the graphs of y = 1/x and y =4/(x - 3) compare?
hint: think of transformations of functions.
3. Jane is organizing a fundraiser to buy a ping-pong table for the community center. The table costs $600.00. Jane is asking contributors to pay for an equal share of the cost of the table. She already has four contributors lined up. What function models the cost per share, C, with respect to the number of new contributors, n? How many new contributors
must Jane recruit in order for the cost of each share to be $25.00?
1. The table represents direct variation. This is because when x doubles, y also doubles. The function to model it is y = 4x.
2. The graph of y = 1/x is a basic hyperbola, while the graph of y = 4/(x - 3) is a transformation of the hyperbola. The second graph is a horizontal shift to the right by 3 units and a vertical stretch by a factor of 4.
3. The function that models the cost per share, C, with respect to the number of new contributors, n, is C = 600 / (4 + n). To find out how many new contributors Jane must recruit in order for each share to cost $25.00, we can set up the equation 25 = 600 / (4 + n) and solve for n. By solving this equation, we find out that Jane must recruit 19 new contributors.