The vertical asymptotes occur when the denominator of the rational function is equal to zero.
To find the vertical asymptotes, set the denominator equal to zero and solve for x:
2x^2 - 7x - 4 = 0
Using the quadratic formula, we get:
x = (7 ± √(7^2 + 4*2*4)) / 4
x = (7 ± √(49 + 32)) / 4
x = (7 ± √81) / 4
x = (7 ± 9) / 4
This gives us two possible vertical asymptotes:
x = (7 + 9) / 4 = 4
x = (7 - 9) / 4 = -1/2
Therefore, the vertical asymptotes for the rational function R(x) are x = 4 and x = -1/2.
Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function. R(x)= (5x^2-19x-4)/ 2x^2-7x-4
Find the vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
1 answer