SOLUTION: Create and describe a function related to kitchen supplies. Give a detailed explanation of the domain (input) and range (output). Then, respond to the following. What values mak

Question 1190482: Create and describe a function related to kitchen supplies. Give a detailed explanation of the domain (input) and range (output). Then, respond to the following.
What values make up the domain? What values make up the range?
Does it make sense for the function to have a root? What would the root describe?
What would the x- and y-intercepts represent for your function?
Does it make sense for your function to have an inverse? Explain.
Describe a situation where your function becomes an equation that can be solved. Solve.
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let's create a function related to kitchen supplies.
**Function:**
Let *C(n)* represent the total cost (in dollars) of purchasing *n* sets of matching kitchen knives. Assume each set of knives costs $45. There is also a flat shipping fee of $8, regardless of the number of knife sets purchased.
So, the function is: C(n) = 45n + 8
**Domain and Range Explanation:**
* **Domain:** The domain represents the possible inputs to the function, in this case, the number of knife sets purchased. Since you can't buy a negative number of knife sets, and we're assuming you buy whole sets of knives, the domain will be non-negative integers.
* **Range:** The range represents the possible outputs of the function, which are the total costs. Since the cost is based on the number of sets purchased, the range will be dollar amounts starting at $8 (the shipping cost) and increasing in increments of $45.
**Domain and Range Values:**
* **Domain:** n = {0, 1, 2, 3, 4, ... } (non-negative integers)
* **Range:** C(n) = {$8, $53, $98, $143, $188, ... } (dollar amounts increasing by $45 from $8)
**Roots:**
Does it make sense for the function to have a root?
No. A root of a function is where the output is zero. In this context, a root would mean the total cost is $0. Since there's a fixed shipping cost of $8, the cost will never be $0, regardless of the number of knife sets purchased.
**Intercepts:**
* **y-intercept:** The y-intercept is where the input (n) is 0. C(0) = 45(0) + 8 = $8. This represents the cost when no knife sets are purchased, which is just the shipping fee.
* **x-intercept:** There is no x-intercept, as explained in the "roots" section.
**Inverse:**
Does it make sense for your function to have an inverse?
Yes. The inverse function would allow you to determine how many knife sets you could buy given a specific budget.
To find the inverse, swap C(n) and n and solve for n:
C = 45n + 8
C - 8 = 45n
n = (C - 8) / 45
So, the inverse function is n(C) = (C - 8) / 45.
**Situation where the function becomes an equation and is solved:**
Situation: You have a budget of $200. How many knife sets can you buy?
Equation: 200 = 45n + 8
Solution:
1. Subtract 8 from both sides: 192 = 45n
2. Divide both sides by 45: n = 192 / 45
3. n ≈ 4.27
Since you can only buy whole sets of knives, you can buy 4 sets of knives with a $200 budget.

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