Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function. R(x)= x^3-8/ x^2-3x+2
Find the vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
Vertical asymptotes occur where the denominator of the rational function equals zero and the numerator does not equal zero.
To find the vertical asymptotes of R(x) = (x^3 - 8) / (x^2 - 3x + 2), we need to find the values of x that make the denominator (x^2 - 3x + 2) equal to zero.
Setting the denominator equal to zero:
x^2 - 3x + 2 = 0
Factoring the quadratic equation:
(x - 1)(x - 2) = 0
Setting each factor equal to zero and solving for x:
x - 1 = 0 or x - 2 = 0
x = 1 x = 2
Therefore, the vertical asymptotes of the function R(x) are x = 1 and x = 2.