Answer
a. $70$, $(30,70)$
b. $70$, same
c. no
Work Step by Step
a. For $x=30$, we have $f(30)=\frac{80(30)-8000}{30-110}=70$ Billion Dollars, which gives a point $(30,70)$ on the graph. (We can also find $f(30)$ from the graph to get 70 Billion Dollars.)
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 $f(30)=80+\frac{800}{30-110}=80-10=70$, 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.
