Polynomial & Rational Functions — Quiz 3

Questions in this quiz (7)

1. Which of the following is equivalent to $$\lim_{x\to\infty}\frac{6x^2}{x^3+3000x}$$?

   • $$0$$
   • $$6$$
   • $$1$$
   • $$\frac{1}{500}$$

2. The graph of which of the following equations has $$y=2$$ as a horizontal asymptote?

   • $$y=\frac{2x+1}{x-3}$$
   • $$y=\frac{x+2}{x+1}$$
   • $$y=\frac{2x^2}{x+1}$$
   • none of these

3. Which of the following functions could represent $$f(x)$$ if $$\lim_{x\to0^-}f(x)=-\infty$$ and $$\lim_{x\to0^+}f(x)=\infty$$?

   • $$f(x)=\frac{1}{x}$$
   • $$f(x)=\frac{-1}{x}$$
   • $$f(x)=\frac{1}{x+1}$$
   • $$f(x)=\frac{1}{x^2+1}$$

4. A rare species of fish was introduced into a lake. The population $$P$$ of the fish $$t$$ months after introduction is $$P(t)=\frac{40(1+0.4t)}{1+0.02t}$$. How many fish were initially introduced?

   • $$20$$
   • $$30$$
   • $$40$$
   • $$60$$

5. A rare species of fish was introduced into a lake. The population $$P$$ of the fish $$t$$ months after introduction is $$P(t)=\frac{40(1+0.4t)}{1+0.02t}$$. What is the largest population the lake can sustain?

   • $$40$$
   • $$800$$
   • $$2000$$
   • none of these

6. Evaluate $$\lim_{n\to\infty}\frac{4n^3-2n}{n^3+5}$$.

   • $$0$$
   • $$4$$
   • $$1$$
   • nonexistent

7. If the graph of $$y=\frac{ax+b}{x+d}$$ has a horizontal asymptote at $$y=3$$ and a vertical asymptote at $$x=-2$$, what is the sum of $$a$$ and $$d$$?

   • $$1$$
   • $$3$$
   • $$5$$
   • $$-1$$