To analyze the function that describes the number of peaches used in relation to the number of pies made, let’s break down the situation:
Kinah makes 40 pies and uses 6 peaches for each pie. Therefore, the total number of peaches used is:
\[ \text{Total peaches} = \text{Number of pies} \times \text{Peaches per pie} = n \times 6 \] where \( n \) is the number of pies.
The domain of this function (the number of pies that Kinah can make) ranges from 0 to 40, as she can make no pies (0) or up to 40 pies.
The range of this function (the total number of peaches used) goes from 0 (if no pies are made) to 240 (if 40 pies are made). To find the range values, we calculate the total number of peaches for each integer \( n \) from 0 to 40. Since she uses 6 peaches per pie, the total would be in the set of multiples of 6:
\[ \text{Total peaches} = 0, 6, 12, 18, \ldots, 240 \]
This shows that the range will be all multiples of 6 between 0 and 240.
Now, looking at the options:
A. The range is the set of all integers from 0 to 40.
- This is incorrect. The range represents the total number of peaches used, not the number of pies.
B. The domain is the set of all integers from 0 to 40.
- This is correct. The number of pies can be any integer value from 0 to 40.
C. The range is the set of all multiples of 6 from 0 to 240.
- This is correct. The total number of peaches used is in multiples of 6 ranging from 0 to 240 (i.e., 0, 6, 12, ..., 240).
D. The domain is the set of all multiples of 6 from 0 to 240.
- This is incorrect. The domain is not restricted to multiples of 6; it simply spans all integers between 0 and 40.
Therefore, the two correct statements are B and C.
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