Find any points of discontinuity for the rational function. y = x-8/x^2 +5x -6
a. x = 8
b. x = –1, x = 6
c. x = 1, x = 6
d. x = 1, x = –6
To find the points of discontinuity for the rational function y = (x - 8) / (x^2 + 5x - 6), we need to look for values of x that make the denominator equal to 0, as division by 0 is undefined.
To find those values, we factor the denominator:
x^2 + 5x - 6 = (x + 6)(x - 1)
Setting this expression equal to 0, we get:
(x + 6)(x - 1) = 0
This leads to two possible values for x:
x = -6 and x = 1
Therefore, the points of discontinuity for the rational function y = (x - 8) / (x^2 + 5x - 6) are x = -6 and x = 1.
The correct answer is:
c. x = 1, x = -6