Graphing a rational function with an absolute value

**rod789** · October 9th 2008, 04:08 PM

f(x)=|x+1|/(x+1)

How do I graph this function?

**Jhevon** · October 9th 2008, 04:11 PM

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?

**rod789** · October 9th 2008, 04:43 PM

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

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