Find the vertical and horizontal asymptotes of the function (y = frac{2x^2 - 3x + 1}{x - 1}).

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Step:1 ：First, simplify the function by dividing both the numerator and denominator by x. We get (y = frac{2x - 3 + frac{1}{x}}{1 - frac{1}{x}}).Step:2 ：As x approaches infinity, (frac{1}{x}) approaches 0. Therefore, the function simplifies to (y = frac{2x - 3}{1}), which is a straight line with a slope of 2 and a y-intercept of -3.Step:3 ：The vertical asymptote is found by setting the denominator equal to zero and solving for x. So, (x - 1 = 0) gives x = 1.Step:4 ：The horizontal asymptote is the line y = 2x - 3.

Answer

Step: 1 ：First, simplify the function by dividing both the numerator and denominator by x. We get (y = frac{2x - 3 + frac{1}{x}}{1 - frac{1}{x}}).Step: 2 ：As x approaches infinity, (frac{1}{x}) approaches 0. Therefore, the function simplifies to (y = frac{2x - 3}{1}), which is a straight line with a slope of 2 and a y-intercept of -3.Step: 3 ：The vertical asymptote is found by setting the denominator equal to zero and solving for x. So, (x - 1 = 0) gives x = 1.Step: 4 ：The horizontal asymptote is the line y = 2x - 3.

Find the vertical and horizontal asymptotes of the function \(y = \frac{2x^2 - 3x + 1}{x - 1}\).

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