contestada

7. The function y = 60 - 8x represents the amount y (in dollars) of money you have arter
buying x movie tickets. (a) Find the domain of the function. Is the domain discrete or continuous
Explain. (b) Graph the function using its domain.

Respuesta :

This function has a couple of restrictions:

  • y can't be less than zero, because when you have no money left you can't buy any more tickets
  • x must be a positive integer, because you can't buy a negative of fractional amount of tickets.

With these constraints in mind, we can explicitly write all the possible (x,y) couples:

[tex]\begin{array}{c|c}x&y\\0&60\\1&52\\2&44\\3&36\\4&28\\5&20\\6&12\\7&4\end{array}[/tex]

Where x is the number of tickets bought and y is the amount of money you're left with. So, if you buy no tickets, you still have all your $60. If you buy 1 ticket you're left with $52. If you buy 2 tickets, you're left with $44, and so on.

This table shows that the domain is the set

[tex]D=\{0,1,2,3,4,5,6,7\}[/tex]

And the range is the set

[tex]R = \{60,52,44,36,28,20,12,4\}[/tex]

And they are both discrete. To graph the function, simply draw all the (x,y) couples on a coordinate grid.