The following piecewise function gives the tax owed, T(x), by a single taxpayer on a taxable income of x dollars.

Screenshot of the function:
http://prntscr.com/14yki3

(i) Determine whether T is continuous at 6061.
(ii) Determine whether T is continuous at 32,473.
(iii) If T had discontinuities, use one of these discontinuities to describe a situation where it might be advantageous to earn less money in taxable income.

Question

The following piecewise function gives the tax owed, T(x), by a single taxpayer on a taxable income of x dollars.

Screenshot of the function:
http://prntscr.com/14yki3

(i) Determine whether T is continuous at  6061.
(ii) Determine whether T is continuous at 32,473.
(iii) If T had discontinuities, use one of these discontinuities to describe a situation where it might be advantageous to earn less money in taxable income.