Question

the linear function y=15x represents the cost y of x tickets for a museum. each customer can buy a max of four tickets.
A: find the domain of the function. is the domain discrete or continuous
B: graph the function using its domain

Answer 1

Interpret x as the number of tickets (whole tickets). Each customer may buy at most 4 tickets.

A.
- Domain: {0, 1, 2, 3, 4} (or {1,2,3,4} if you disallow buying 0 tickets).
- The domain is discrete (only whole-number ticket amounts are allowed).

Also the range (costs) is {0, 15, 30, 45, 60}.

B.
Points to plot (x, y = 15x): (0,0), (1,15), (2,30), (3,45), (4,60).
Plot these five points on the xy-plane. They lie on the straight line y = 15x, but only the five discrete points are part of the graph because the domain is discrete. (If fractional tickets were allowed, the graph would be the continuous line segment from x = 0 to x = 4.)