(Section 2.4: Limits and Infinity II) 2.4.6 Finding VAs for Graphs of Rational Functions (Expressed in Simplified Form)If: • fx()is rational and written in the form =NxDx, • and are polynomials, • ±0(i.e., the zero polynomial), and • and have no real zeros in common; i.e., they have no variable factors in common. Then: The graph of y=has a VA at x=a(and limx±a+=²or³², and limx±a²=³or²³) ±ais a real zero of . Example 4 (Revisiting Example 3)Let =x+1x2+4x. Find the equations of the vertical asymptotes (VAs) of the graph of y=in the xy-plane. Justify your answer using limits. Solution Methodx+1x2+4x=x+1xx+4. Observe that the numerator and the denominator have no variable factors (and no real zeros) in common. Therefore,
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.