(Section 2.3: Limits and Infinity I) 2.3.22 “Zoom Out” Property of HAs and SAsIf we keep expanding the scope of the window of a grapher, then a graph with a HA or a SA will generally look more and more like the HA or SA. Example 16Analyze the “long-run” behavior of the graph of fx()=±4x7+12x6+5x4±23x3+114x3±5. SolutionBy Dominant Term Substitution, we find that: limx±²=limx³4x74x3=limx³x4=³²limx±²³=limx²4x74x3=limx²x4=²³If we perform Long Division, we obtain: =±x4+3x3±2+14x3±5. The graph of y=±x4+3x3±2is a nonlinear asymptote that the
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