Chapter 1.4, Problem 66E

Learning theory. In 1917, L. L. Thurstone, a pioneer in quantitative learning theory, proposed the rational function

  $f(x)=\frac{a(x+c)}{(x+c)+b}$

to model the number of successful acts per unit time that a person could accomplish after x practice sessions. Suppose that for a particular person enrolled in a typing class,

  $f(x)=\frac{55(x+1)}{(x+8)}x\ge 0$

where f(x) is the number of words per minute the person is able to type after x weeks of lessons.

1. (A)   What does f(x) approach as x increases?
2. (B)   Sketch a graph of function f, including any vertical or horizontal asymptotes.