find the horizontal and vertical asymptotes of the curve. you may want to use a graphing calculator or…

find the horizontal and vertical asymptotes of the curve. you may want to use a graphing calculator or computer. (enter your answers as comma - separated lists. if an answer does not exist, enter dne.)\n$y = \\frac{2x^{2}+3}{3x^{2}+8x - 3}$\n$x = $\n$y = $\nresources\nread it\nmaster it\nsubmit answer

find the horizontal and vertical asymptotes of the curve. you may want to use a graphing calculator or computer. (enter your answers as comma - separated lists. if an answer does not exist, enter dne.)\n$y = \\frac{2x^{2}+3}{3x^{2}+8x - 3}$\n$x = $\n$y = $\nresources\nread it\nmaster it\nsubmit answer

Answer

Explanation:

Step1: Find vertical asymptotes

Set denominator (3x^{2}+8x - 3=0). Factor: ((3x - 1)(x + 3)=0). Solve: (x=\frac{1}{3}) or (x=-3).

Step2: Find horizontal asymptotes

Degree of numerator (n = 2), degree of denominator (m = 2). Since (n=m), (y=\frac{\text{leading coefficient of numerator}}{\text{leading coefficient of denominator}}). Leading coefficient of numerator is (2), of denominator is (3). So (y=\frac{2}{3}).

Answer:

(x=-3,\frac{1}{3}) (y=\frac{2}{3})