Chapter 2.4, Problem 55PE

During the 1980s, the controversial economist Arthur Laffer promoted the idea that tax increases lead to a reduction in government revenue. Called supply-side economics, the theory uses functions such as

$f(x)=\frac{80x-8000}{x-110},30\le x\le 100$

This function models the government tax revenue, f(x), in lens of billions of dollars, in terms of the tax rate x the graph of the function is shown. It illustrates tax revenue decreasing quite dramatically as the tax rate increase. At a tax rate of (gasp) 100%, the government takes all our money and no one has an incentive to work. With no income earned, zero dollars in tax revenue is generated.

a. Find and interpret f (30). Identify the solution as a point on the graph of the function.

b. Rewrite the function by using long division to perform $(80x-8000)÷(x-110)$

Then use this new form of the function to find f (30). Do you obtain the same answer as you did in part (a)?

c. Is f a polynomial function? Explain your answer.