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.
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.
1 answer