Sketch the graph of a function {{MATH_136}} which has the following properties: {{CMD_137}} {{CMD_138}} {{MATH_139}} {{CMD_140}} {{MATH_141}} {{CMD_142}} {{MATH_143}} {{CMD_144}} {{MATH_145}} {{CMD_146}} {{MATH_147}} on {{MATH_148}} {{CMD_149}} {{MATH_150}} on {{MATH_151}} {{CMD_152}} {{MATH_153}} on {{MATH_154}} {{CMD_155}} {{MATH_156}} on {{MATH_157}} {{CMD_158}} {{MATH_159}} on {{MATH_160}} {{CMD_161}} {{CMD_162}} Try this on your own first, then either check with a friend or check the online version. {{CMD_163}} The first thing we will do is to plot the points {{MATH_164}} and {{MATH_165}}, and the ``holes" at {{MATH_166}} and {{MATH_167}} due to the limit conditions. We can immediately draw in what {{MATH_168}} looks like on {{MATH_169}} since it is linear with slope {{MATH_170}}, and must connect to the hole at {{MATH_171}}. We also mark all of the places where {{MATH_172}} or {{MATH_173}} change sign. {{CMD_174}} {{ENV_175}} {{CMD_176}} {{CMD_177}}