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3 problems match “horizontal asymptotes”. Clear

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  1. Degree of numerator for horizontal asymptote ●○○○○ 10 ptsThe graph of the rational function q(x)2x5+x4−7x2+1\frac{q(x)}{2x^5+x^4-7x^2+1} has a horizontal asymptote. What is the largest possible degree of q(x)q(x)?
  2. Horizontal asymptote of a rational function ●○○○○ 10 ptsAt what value of yy is there a horizontal asymptote for the graph of the equation y=4x3+2x−43x3−2x2+5x−1y=\frac{4x^3+2x-4}{3x^3-2x^2+5x-1}? Round to two decimal places.
  3. Crossing the horizontal asymptote ●●○○○ 20 ptsFor which value of xx does the function f(x)=2x2−5x−7x2−4x+1f(x) = \frac{2x^2 - 5x - 7}{x^2 - 4x + 1} cross its horizontal asymptote?