What are the points of discontinuity?
y =(x-2)/(x^2 + 5x - 6)
A. x = 6, x = –1
B. x = 1, x = 6
C. x = –6, x = 1
D. x = 8
A. x = 6, x = –1
To find the points of discontinuity in the given function, we need to identify the values of x where the function is undefined. In this case, the function is undefined when the denominator (x^2 + 5x - 6) is equal to zero.
To find the values of x that make the denominator zero, we can set it equal to zero and solve for x:
x^2 + 5x - 6 = 0
Factoring the quadratic equation, we have:
(x - 1)(x + 6) = 0
Setting each factor equal to zero, we get:
x - 1 = 0, x + 6 = 0
Solving these equations, we find:
x = 1, x = -6
Therefore, the points of discontinuity in the given function are x = 1 and x = -6.
Hence, the correct answer is C. x = –6, x = 1.