In New York state in 2010, the income tax rates for a single person were as follows:

4% of the first $8000 earned,

4.5% of the next $3000 earned,

5.25% of the next $2000 earned,

5.9% of the next $7000 earned,

6.85% of the next $180,000 earned,

7.85% of the next $300,000 earned, and

8.97% of any amount earned over $500,000.

Let f (x) represent the amount of tax owed on an income of x dollars. Find each of the following, and explain in a sentence what the answer tells you.

a. f(10,000)

b. f(12,000)

c. f(18,000)

d. Sketch a graph of f(x).