What are the vertical asymptotes of the function f(x) = (x^2 + 1)/(3x - 2x^2)

2 Answers

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The vertical asymptotes of a function f(x) = A/B are the lines with equation x = a, where a is the roots of the denominator B.

For the function f(x) = (x^2 + 1)/(3x - 2x^2), the denominator is 3x - 2x^2.

The roots of 3x - 2x^2 are the solutions of the equation

3x - 2x^2 = 0

x(3 - 2x) = 0

x = 0 and x = 3/2

The vertical asymptotes of the function are x = 0 and x = 3/2.

The graph of the function verifies the same.

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balajia | College Teacher | (Level 1) eNoter

Posted on

to get the vertical symptotes just equate the denominator to zero.

that is 3x-2x^2=0

the vertical asympoyes are x=0 and x=3/2