In the given equation, y represents the total cost, and x represents the number of bars of soap ordered. You are told that Sy will order a minimum of 5 bars of soap and a maximum of 8 bars of soap. This information helps us determine the domain and range.
**Domain:** The domain is the set of all possible values for the independent variable (x), in this case, the number of bars of soap ordered. Sy will order a minimum of 5 bars and a maximum of 8 bars, so the domain can be expressed as:
Domain: 5 ≤ x ≤ 8
This means x can take any value between 5 and 8, including 5 and 8.
**Range:** The range is the set of all possible values for the dependent variable (y), in this case, the total cost. To find the range, you can use the equation:
y = 2.75x + 3
Now, you need to consider the minimum and maximum values of x within the given domain (5 to 8) and calculate the corresponding values of y:
1. For x = 5:
y = 2.75(5) + 3 = 13.75 + 3 = 16.75
2. For x = 8:
y = 2.75(8) + 3 = 22 + 3 = 25
So, within the specified domain, the range of y is:
Range: y
This means y can take any value between 16.75 and 25, including 16.75 and 25, corresponding to the minimum and maximum values of x in the given domain.