Practical Domain of the Function

Oct 13, 2025 by windailys.com 98 views

Understanding the Function

The function ${$ f(x) $}$ represents the total amount spent at a store when purchasing ${$ x $}$ items that are $5 each, with no tax. This means that the function takes the number of items purchased as input and returns the total amount spent as output.

Practical Domain of the Function

The practical domain of a function refers to the set of all possible input values for which the function is defined and produces a valid output. In the case of the function ${$ f(x) $}$, the input value is the number of items purchased, and the output value is the total amount spent.

Analyzing the Function

To determine the practical domain of the function ${$ f(x) $}$, we need to consider the following:

The number of items purchased cannot be negative, as it is not possible to purchase a negative number of items.
The number of items purchased cannot be a fraction, as it is not possible to purchase a fraction of an item.
The number of items purchased cannot be a very large number, as it is not possible to purchase an infinite number of items.

Determining the Practical Domain

Based on the above analysis, we can conclude that the practical domain of the function ${$ f(x) $}$ is the set of all positive integers that are less than or equal to the maximum number of items that can be purchased.

Maximum Number of Items

The maximum number of items that can be purchased is not specified in the problem. However, in a real-world scenario, there is a limit to the number of items that can be purchased. For example, a store may have a maximum limit on the number of items that can be purchased in a single transaction.

Assuming a Maximum Limit

For the purpose of this problem, let's assume that the maximum number of items that can be purchased is 1000. This is a reasonable assumption, as most stores have a maximum limit on the number of items that can be purchased in a single transaction.

Practical Domain

Based on the above assumption, the practical domain of the function ${$ f(x) $}$ is the set of all positive integers that are less than or equal to 1000.

Conclusion

In conclusion, the practical domain of the function ${$ f(x) $}$ is the set of all positive integers that are less than or equal to the maximum number of items that can be purchased. This is a reasonable assumption, as most stores have a maximum limit on the number of items that can be purchased in a single transaction.

Example Use Cases

Here are a few example use cases for the function ${$ f(x) $}$:

A customer purchases 5 items, and the total amount spent is ${$ f(5) = 5 \times 5 = 25 $}$.
A customer purchases 10 items, and the total amount spent is ${$ f(10) = 10 \times 5 = 50 $}$.
A customer purchases 100 items, and the total amount spent is ${$ f(100) = 100 \times 5 = 500 $}$.

Code Implementation

Here is a simple code implementation of the function ${$ f(x) $}$ in Python:

def total_amount_spent(x):
    """
    This function calculates the total amount spent at a store when purchasing x items that are $5 each, with no tax.
Args:
    x (int): The number of items purchased.

Returns:
    int: The total amount spent.
&quot;&quot;&quot;
if x &lt; 0:
    raise ValueError(&quot;The number of items purchased cannot be negative.&quot;)
if x &gt; 1000:
    raise ValueError(&quot;The number of items purchased cannot exceed 1000.&quot;)
return x * 5

Testing the Function

Here are a few test cases for the function ${$ f(x) $}$:

print(total_amount_spent(5))  # Output: 25
print(total_amount_spent(10))  # Output: 50
print(total_amount_spent(100))  # Output: 500

Conclusion

Q: What is the function ${$ f(x) $}$ used for?

A: The function ${$ f(x) $}$ is used to calculate the total amount spent at a store when purchasing ${$ x $}$ items that are $5 each, with no tax.

Q: What is the practical domain of the function ${$ f(x) $}$?

A: The practical domain of the function ${$ f(x) $}$ is the set of all positive integers that are less than or equal to the maximum number of items that can be purchased.

Q: What is the maximum number of items that can be purchased?

A: The maximum number of items that can be purchased is not specified in the problem. However, for the purpose of this problem, let's assume that the maximum number of items that can be purchased is 1000.

Q: Can the number of items purchased be a fraction?

A: No, the number of items purchased cannot be a fraction, as it is not possible to purchase a fraction of an item.

Q: Can the number of items purchased be negative?

A: No, the number of items purchased cannot be negative, as it is not possible to purchase a negative number of items.

Q: How is the function ${$ f(x) $}$ implemented in Python?

A: The function ${$ f(x) $}$ can be implemented in Python as follows:

def total_amount_spent(x):
    """
    This function calculates the total amount spent at a store when purchasing x items that are $5 each, with no tax.
Args:
    x (int): The number of items purchased.

Returns:
    int: The total amount spent.
&quot;&quot;&quot;
if x &lt; 0:
    raise ValueError(&quot;The number of items purchased cannot be negative.&quot;)
if x &gt; 1000:
    raise ValueError(&quot;The number of items purchased cannot exceed 1000.&quot;)
return x * 5

Q: How can the function ${$ f(x) $}$ be tested?

A: The function ${$ f(x) $}$ can be tested with various input values, such as:

print(total_amount_spent(5))  # Output: 25
print(total_amount_spent(10))  # Output: 50
print(total_amount_spent(100))  # Output: 500

Q: What are some example use cases for the function ${$ f(x) $}$?

A: Some example use cases for the function ${$ f(x) $}$ include:

A customer purchases 5 items, and the total amount spent is ${$ f(5) = 5 \times 5 = 25 $}$.
A customer purchases 10 items, and the total amount spent is ${$ f(10) = 10 \times 5 = 50 $}$.
A customer purchases 100 items, and the total amount spent is ${$ f(100) = 100 \times 5 = 500 $}$.

Q: What are some potential errors that can occur when using the function ${$ f(x) $}$?

A: Some potential errors that can occur when using the function ${$ f(x) $}$ include:

The number of items purchased is negative.
The number of items purchased exceeds the maximum limit.
The input value is not an integer.

Q: How can the function ${$ f(x) $}$ be modified to handle these errors?

A: The function ${$ f(x) $}$ can be modified to handle these errors by adding error checking code, such as:

def total_amount_spent(x):
    """
    This function calculates the total amount spent at a store when purchasing x items that are $5 each, with no tax.
Args:
    x (int): The number of items purchased.

Returns:
    int: The total amount spent.
&quot;&quot;&quot;
if not isinstance(x, int):
    raise ValueError(&quot;The number of items purchased must be an integer.&quot;)
if x &lt; 0:
    raise ValueError(&quot;The number of items purchased cannot be negative.&quot;)
if x &gt; 1000:
    raise ValueError(&quot;The number of items purchased cannot exceed 1000.&quot;)
return x * 5

Conclusion

In conclusion, the function ${$ f(x) $}$ is used to calculate the total amount spent at a store when purchasing ${$ x $}$ items that are $5 each, with no tax. The practical domain of the function is the set of all positive integers that are less than or equal to the maximum number of items that can be purchased. The function can be implemented in Python and tested with various input values.