the domain is:
{0, 1, 2, 3, 4, 5}
And the range is:
{50, 41, 32, 23, 14, 5}
For a relation that maps elements x into elements y, we define the domain as the set of inputs (the elements x) and the range as the set of outputs (the elements y).
In this case, we know that Liam can spend a maximum of $50, so let's define:
y = Liam's money.
x = number of movies that he buys.
We can write:
y = $50 - $9*x
The maximum number of movies that he can buy is when his money reaches zero, so:
0 = $50 - $9*x
$9*x = $50
x = $50/$ 9 = 5.6
Rounding downwards, we conclude that x = 5 is the maximum number of movies that he can buy.
Then the domain is:
{0, 1, 2, 3, 4, 5}
And the range the set of the values of y associated to these values of x, it is:
{50, 41, 32, 23, 14, 5}
If you want to learn more about domain and range:
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