Chapter 2.1, Problem 89E

Let f be defined by

$f(x)=\{\begin{array}{ll}1+mx\hfill & \text{if}x\le 1\hfill \\ 4-mx\hfill & \text{if}x>1\hfill \end{array}$

where m is a constant.

1. (A)   Graph f for m = 1, and find

   $\begin{array}{lll}\underset{x\to 1^{-}}{\lim }f(x)\hfill & \text{and}\hfill & \underset{x\to 1^{+}}{\lim }f(x)\hfill \end{array}$

1. (B)   Graph f for m = 2, and find

   $\begin{array}{lll}\underset{x\to 1^{-}}{\lim }f(x)\hfill & \text{and}\hfill & \underset{x\to 1^{+}}{\lim }f(x)\hfill \end{array}$

1. (C)   Find m so that

      $\underset{x\to 1^{-}}{\lim }f(x)=\underset{x\to 1^{+}}{\lim }f(x)$

    and graph f for this value of m.

1. (D)   Write a brief verbal description of each graph. How does the graph in part (C) differ from the graphs in parts (A) and (B)?