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\noindent {\bf Problem statement} The income tax rate is the percent
of income which is owed to the government. For example, if the tax
rate is 7\%, then the tax owed on an income of \$10,000 is
\$700. Many governments have progressive income taxes, which have
varying tax rates which increase when income increases.

In the country of Bxwy, the tax rate on income below \$10,000 is 0\%,
the tax rate on income between \$10,000 and \$30,000 is 4\%, the tax
rate on income between \$30,000 and \$75,000 is 12\%, the tax rate on
income between \$75,000 and \$120,000 is 19\%, and the tax rate on
income above \$120,000 is 25\%. The tax law also states that the total
tax owed must be a continuous function of income.

Describe the (piecewise-defined) function $f(x)$ as clearly as
possible by formulas. Here $x$ is the income of a resident of Bxwy,
and $f(x)$ is the tax owed on that income. Graph $y=f(x)$ for $x$
between 0 and 150,000.







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