MAC1105 Lecture 20: 5.3 The Graph Of A Rational Function Notes
16 Feb 2017
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5. 3 the graph of a rational function notes: sterling. Provide a generalization to the terms listed in this section. Domain: the set of all possible input values. Example : x4 10x2 + 9 = 0 u2 10u + 9 = 0 (u 1) (u 9) = 0 u = 1, 9 x2 = 9. X2 = 9 x = 3 x2 = 1. Holes are removable discontinuities and occur when any value is unde ned when solved, but normally occurs when you have fractions with a variable in the denominator. Find the graph"s intercepts [if any]: x-intercepts. Substitute 0 for y, which is f (x). Solve for the x variable: y -intercepts. Determine any odd and/or even multiplicities: odd: crossing the x-axis at the given point, even: tangent to the x-axis at the given point. Vertical asymptotes are lines that have an equation in the form of x = h.
