A bike rental company charges a nonrefundable deposit of $15

Question

for a bike rental plus $5
for every day of the rental, where each portion of a day is rounded to a full day. A rental can last for no less than 1
day and no more than 2
weeks, and f (x)
represents the total cost of the rental, where
represents the number of days the rental lasts.

What is the most appropriate domain for the situation, when graphed on a coordinate plane?

Answer 1

To define the appropriate domain for the bike rental situation described, we need to consider the number of days the rental lasts, denoted as \( x \).

According to the problem:

• A bike rental can last for no less than 1 day and no more than 2 weeks.
• 1 week has 7 days, so 2 weeks equals \( 2 \times 7 = 14 \) days.

This means the number of days \( x \) must satisfy the following conditions:

• The minimum value of \( x \) is 1 (for 1 day).
• The maximum value of \( x \) is 14 (for 14 days).

Thus, the domain of the function \( f(x) \) that represents the total cost of the rental is: \[ x \in [1, 14] \]

In conclusion, the most appropriate domain for \( x \) when graphed on a coordinate plane is: \[ \text{Domain: } [1, 14] \]

Answer 2

20 ≤ ≤ x ≤ ≤ 85

{ 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 , 85 }

1 ≤ ≤ x ≤ ≤ 14

Answer 3

It appears that you're specifying ranges of values or constraints in a somewhat fragmented format. Let's break this down into two parts based on your statements and clarify them.

1. First Range: \( 20 \leq x \leq 85 \)

You seem to be indicating that \( x \) can take specific values in the range from 20 to 85, which includes the following values:

• { 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85 }

2. Second Range: \( 1 \leq x \leq 14 \)

In this context, the second range specifies that \( x \) can take values from 1 to 14, which is likely related to the bike rental situation previously discussed.

Combined Interpretation

It seems like you are perhaps trying to illustrate two different contexts or ranges for \( x \). To clarify:

• For the bike rental context: \[ 1 \leq x \leq 14 \quad \text{(where \( x \) represents the number of days rented)} \] Possible values for \( x \) in this context are: { 1, 2, 3, ..., 14 }

• For another context (which is not specified): \[ 20 \leq x \leq 85 \quad \text{(possibly representing another variable with specified values)} \] Possible values for \( x \) here are: { 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85 }

Conclusion

If you are describing two different scenarios, ensure to specify the context for each, as they serve different purposes. Each range can be interpreted separately. If you need a further analysis or a specific application for either set of values, please provide more context!

Answer 4

last answer is {1, 2, 3, 4, 5, 6 , 7, 8, 9, 10, 11, 12, 13, 14}

Answer 5

Thank you for the clarification!

For the bike rental scenario where \( x \) represents the number of days the rental lasts and can take values from 1 to 14 days, the appropriate set of possible integer values is as follows:

\[ { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 } \]

This set indeed represents all the possible discrete values for \( x \) in the context of the bike rental situation.

To summarize:

• The domain for the bike rental cost function in integer form is: \[ { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 } \]

If you need further assistance or have more questions, feel free to ask!