# Chapter 2 - Section 2.4 - Dividing Polynomials; Remainder and Factor Theorems - Exercise Set - Page 365: 56

a. $68.6$, $(40,68.6)$ b. $68.6$, same c. no

#### Work Step by Step

a. For $x=40$, we have $f(40)=\frac{80(40)-8000}{40-110}\approx68.6$ Billion Dollars at a tax rate of $40\%$, which gives a point $(40,68.6)$ on the graph. b. Performing the long division as shown in the figure, we get $f(x)=80+\frac{800}{x-110}$. From this new form, we have $f(40)=80+\frac{800}{40-110}=80-10\approx68.6$, which agrees with the result from part-a. c. Function $f$ is a rational function, which is the ratio of two polynomial functions; thus $f$ is not a polynomial function.

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