Question

In the function f(x) = 35x + 20, what does the x represent?

A. The amount Margo charges per hour
B. The number of hours Margo worked
C. The fixed service fee
D. The total cost of repair

Answer 1

In the linear function f(x) = 35x + 20, the variable x represents the number of hours Margo worked, with the function describing a $35 per hour charge in addition to a fixed $20 service fee.

Step-by-step explanation:

In the function f(x) = 35x + 20, the variable x represents the number of hours Margo worked. This equation is an example of a linear function that models a real-world situation where a charge is based on a fixed fee plus a fee that depends on the amount of time worked. The fixed service fee is represented by the constant term (20), while the variable term (35x) indicates that Margo charges $35 for each hour worked.

The general form for such functions is y = mx + b, where m is the slope representing the rate of charge per hour (in this case $35/hour), and b is the y-intercept representing the fixed service fee (in this case, $20).

Answer 2

The variable x in the function f(x) = 35x + 20 represents B. The number of hours Margo worked. So, Option B is correct.

Step-by-step explanation:

In the given function f(x) = 35x + 20, the variable x represents the number of hours Margo worked. The coefficient 35 attached to x signifies the hourly rate Margo charges for her services. Therefore, when you multiply the number of hours worked (x) by the hourly rate (35), you get the total cost of Margo's services. The constant term 20 in the function represents any fixed service fee or additional cost that Margo charges, regardless of the number of hours worked.

For instance, if Margo worked for 2 hours, the calculation would be f(2) = 35 * 2 + 20 = 70 + 20 = 90. This means that Margo would charge a total of 90 for 2 hours of work, including the fixed service fee. In this context, x represents the variable input (number of hours), and the function output (f(x)) gives the total cost of Margo's services.

In summary, the function f(x) = 35x + 20 encapsulates the relationship between the number of hours Margo worked (x) and the total cost of her services. The variable x is the key factor that determines the output, making it a representation of the hours worked by Margo.