Could you help me with answering the following questions?

Questions:

Answer the following questions:

1. Can the graph of a function have no x-intercepts? Two x-intercepts? Infinitely many x-intercepts? Give examples to support your answer.

2. Can the graph of a function have more than one y-intercepts? Justify your answer. (Hint: Go back to the definition of a function)

3. A piecewise function is a function in which the formula used depends upon the domain the input lies in. We notate this idea like this:

Tax bracket is an example of piece-wise function where the tax paid by the individual is determined by the specific amount of taxable income. Below is the marginal tax rate for the year 2021 for individual single taxpayer

Marginal Tax Rate : Source IRS

• 37% for incomes greater than $523,600
• 35% for incomes over $209,425
• 32% for incomes over $164,925
• 24% for incomes over $86,375
• 22% for incomes over $40,525
• 12% for incomes over $9,950
• 10% for incomes $9,950 or less

a. Come up with a formula for finding the tax using f(x) as the amount of tax to be paid by individual single taxpayer with adjusted taxable income x

b. Sketch a graph of this function? What can you say about the behavior of this graph and the relationship between the income and the amount of tax.

c. How much would a single taxpayer pay for tax if the income is $ 90,000 or

f (90,000)?