What are the points of discontinuity?
y=(x-2)/(x^(2)+5x-6)
The points of discontinuity are the values of x that make the denominator of the function equal to zero.
To find these values, we factor the denominator:
x^2 + 5x - 6 = (x + 6)(x - 1)
The denominator equals zero when x = -6 or x = 1. Therefore, the points of discontinuity are x = -6 and x = 1.
To find the points of discontinuity for the given function y=(x-2)/(x^2+5x-6), we need to determine the values of x that make the denominator equal to zero. When the denominator equals zero, the function is undefined, resulting in points of discontinuity.
The denominator of the function is x^2+5x-6. To find the values of x that make the denominator zero, we can solve the quadratic equation:
x^2 + 5x - 6 = 0
To solve this equation, we can factor it. After factoring, we get:
(x + 6)(x - 1) = 0
Setting each factor equal to zero gives us the values of x that make the denominator zero:
x + 6 = 0 --> x = -6
x - 1 = 0 --> x = 1
Therefore, the points of discontinuity for the given function are x = -6 and x = 1.