In New York state in 2019, the income tax rates for a single person were as follows:
4% of the first $8500 earned,
4.5% of the next $3200 earned,
5.25% of the next $2200 earned,
5.9% of the next $7500 earned,
6.33% of the next $59,250 earned,
6.57% of the next $134,750 earned,
6.85% of the next $862,150 earned, and
8.82% of any amount earned over $1,077,550.
Let ƒ(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. Source: New York State.
(a) ƒ(10,000)
(b) ƒ(12,000)
(c) ƒ(18,000)
(d) ƒ(50,000)
(e) Find the domain and range of ƒ(x).
(f) Sketch a graph of ƒ(x) for 0 ≤ x ≤ 100,000.