Taxes The table below gives the income tax due, f(x), on each given taxable income, x . Taxable Income

Taxes

The table below gives the income tax due, f(x), on each given taxable income, x .

Taxable Income (dollars)	Income Tax Due (dollars)
63,700	8779
63,800	8804
63,900	8829
64,000	8854
64,100	8879
64,200	8904
64,300	8929

What is the domain and range of the function in the table?
Create a scatterplot of the data.
Do the points appear to lie on a line?
Do the inputs change by the same amount? Do the outputs change by the same amount?
Is the rate of change in tax per $1 of income constant? What is the rate of change?
Will a linear function fit the data points exactly?
Write a linear function y = g(x) that fits the data points.
Verify that the linear model fits the data points by evaluating the linear function at x = 63,900 and x = 64,100 and comparing the resulting y-values with the income tax due for these taxable incomes.
Is the model a discrete or continuous function?
Can the model be used to find the tax due on any taxable income between 63,700 and 64,300?
What is the tax due on a taxable income of 64,150, according to this model?

Cost, Revenue, Profit

The following table gives the weekly revenue and cost, respectively, for a selected number of units of production and sale of a product by the Quest Manufacturing Company.

Number of Units	Revenue ($)	Number of Units	Cost ($)
100	6800	100	32,900
300	20,400	300	39,300
500	34,000	500	46,500
900	61,200	900	63,300
1,400	95,200	1,400	88,800
1,800	122,400	1,800	112,800
2,500	170,000	2,500	162,500

Provide the information requested and answer the questions.

Use technology to determine the functions that model revenue and cost functions for this product, using x as the number of units produced and sold.

a) Combine the revenue and cost functions with the correct operation to create the profit function for this product.
b) Use the profit function to complete the following table:

x (units)	Profit, P(x) ($)
0
100
600
1600
2000
2500

Find the number of units of this product that must be produced and sold to break even.
Find the maximum possible profit and the number of units that gives the maximum profit.

a) Use operations with functions to create the average cost function for the product.
b) Complete the following table:

x (units)	Average Cost, C(x) ($/unit)
1
100
300
1400
2000
2500

c) Graph this function using the viewing window [0,2500] by [0,400].

Graph the average cost function using the viewing window [0,4000] by [0,100]. Determine the number of units that should be produced to minimize the average cost.
Compare the number of units that produced the minimum average cost with the number of units that produced the maximum profit. Are they the same number of units? Discuss which of these values is more important to the manufacturer and why.