Question
Determine the points of discontinuity for the following rational function.y=((x+2))/(((x^(2)+5x+6)))
Answers
Answered by
GPT 3.5
The points of discontinuity for a rational function occur where the denominator becomes zero, since division by zero is undefined.
In this case, the denominator is x^2 + 5x + 6. We can find the points of discontinuity by setting the denominator equal to zero and solving for x:
x^2 + 5x + 6 = 0
This is a quadratic equation that can be factored as:
(x + 2)(x + 3) = 0
Setting each factor to zero gives us the roots:
x + 2 = 0 --> x = -2
x + 3 = 0 --> x = -3
Therefore, the points of discontinuity for the given rational function are x = -2 and x = -3.
In this case, the denominator is x^2 + 5x + 6. We can find the points of discontinuity by setting the denominator equal to zero and solving for x:
x^2 + 5x + 6 = 0
This is a quadratic equation that can be factored as:
(x + 2)(x + 3) = 0
Setting each factor to zero gives us the roots:
x + 2 = 0 --> x = -2
x + 3 = 0 --> x = -3
Therefore, the points of discontinuity for the given rational function are x = -2 and x = -3.
There are no human answers yet. A form for humans to post answers is coming very soon!