Let's go through each part of the question step by step:
### Part a: What is the cost of 4 peanut butter jars?
To find the cost of 4 peanut butter jars, we use the provided equation [tex]\( C(x) = 2.50x \)[/tex], where [tex]\( x \)[/tex] is the number of jars and [tex]\( C(x) \)[/tex] is the total cost.
1. Substitute [tex]\( x = 4 \)[/tex] into the equation:
[tex]\[
C(4) = 2.50 \times 4
\][/tex]
2. Calculate the product:
[tex]\[
C(4) = 10.00
\][/tex]
So, the cost of 4 peanut butter jars is [tex]\( \$10.00 \)[/tex].
### Part b: Why is -2 not in the domain?
The domain of a function represents all the possible input values (in this case, the number of peanut butter jars) for which the function is defined.
1. The number of peanut butter jars [tex]\( x \)[/tex] must be a non-negative number:
- You cannot buy a negative number of jars, as it is not physically possible to have a negative quantity of a product.
- Negative values do not make sense in the context of this problem.
Therefore, [tex]\( x = -2 \)[/tex] is not in the domain because it is illogical to purchase a negative amount of jars.
### Part c: Why is 5.5 not in the domain?
Similarly, the number of jars [tex]\( x \)[/tex] typically must be a whole number:
1. Jars of peanut butter are usually sold in whole units.
- You cannot buy a fraction of a jar in most retail situations.
- Partial jars are not commonly available for purchase, which means [tex]\( x \)[/tex] should be an integer.
Therefore, [tex]\( x = 5.5 \)[/tex] is not in the domain because you cannot generally purchase half a jar of peanut butter, and the context assumes whole units.
### Summary:
- Part a: The cost of 4 jars is [tex]\( \$10.00 \)[/tex].
- Part b: -2 is not in the domain because you cannot buy a negative quantity of jars.
- Part c: 5.5 is not in the domain because you typically cannot buy partial jars in retail.
These explanations clarify the constraints and logical bounds applied to the equation and domain of the function [tex]\( C(x) = 2.50x \)[/tex] in this practical context.
