The domain and the range of the function describes the possible profit or
loss from the sale of popcorn and the number of popcorn units.
The correct responses are;
- C. The function is <u>discrete</u>
- D. The function is; <u>y = 1.5·x - 32</u>
- E. The domain is; <u>0 ≤ x ≤ 150</u>
- F. The loss when non of the popcorn is sold is <u>$-32</u>
- G. The profit is<u> $193</u>
- H. The range is;<u> -32 ≤ y ≤ 193</u>
Reasons:
The question parameters are;
The price of a popcorn = $1.5
Number of popcorn he purchases = 150
Total profit made = $5.50
The number of containers sold = 25
Therefore;
C. Given that the number of containers sole is countable, the function will be <u>discrete</u>.
D. Cost of the containers = Revenue - Profit
Which gives;
Cost of the containers = 1.5 × 25 - 5.5 = 32
The given function is therefore;
<u>y = 1.5·x - 32</u>
E. The domain is the 150 containers which gives;
The domain =<u> 0 ≤ x ≤ 150</u>
F. When no popcorn is sold, we have;
x = 0, which gives;
y = 1.5 × 0 - 32 = -32
If he does not sell any popcorn, the loss is $32
G. If all the popcorn are sold, we have;
x = 150
Therefore;
y = 1.5 × 150 - 32 = 193
The profit if all the popcorn are sold = <u>$193</u>
H. The range of the function are the possible <em>y</em> values, which is the possible profit or loss, which gives;
The range =<u> -32 ≤ y ≤ 193</u>
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