# Graphing a rational function with an absolute value

• Oct 9th 2008, 04:08 PM
rod789
Graphing a rational function with an absolute value
f(x)=|x+1|/(x+1)

How do I graph this function?
• Oct 9th 2008, 04:11 PM
Jhevon
Quote:

Originally Posted by rod789
f(x)=|x+1|/(x+1)

How do I graph this function?

remember, $|x| = \left \{ \begin{array}{lr}x & \mbox{ if } x \ge 0 \\ & \\ -x & \mbox{ if } x < 0 \end{array} \right.$

so, $f(x) = \frac {|x + 1|}{x + 1} = \left \{ \begin{array}{lr} \frac {x + 1}{x + 1} = 1 & \mbox{ if } x + 1 \ge 0 \\ & \\ \frac {-(x + 1)}{x + 1} = -1 & \mbox{ if } x + 1 < 0 \end{array} \right.$

can you continue?
• Oct 9th 2008, 04:43 PM
rod789
Quote:

Originally Posted by Jhevon
remember, $|x| = \left \{ \begin{array}{lr}x & \mbox{ if } x \ge 0 \\ & \\ -x & \mbox{ if } x < 0 \end{array} \right.$

so, $f(x) = \frac {|x + 1|}{x + 1} = \left \{ \begin{array}{lr} \frac {x + 1}{x + 1} = 1 & \mbox{ if } x + 1 \ge 0 \\ & \\ \frac {-(x + 1)}{x + 1} = -1 & \mbox{ if } x + 1 < 0 \end{array} \right.$

can you continue?

yeah, thanks