Question

If a hole exists for this function, identify its location.

f(x) = x^2 + 5x + 6 / x^2 + 3x + 2

a. x = -1
b. x = -2
c. x = -3
d. No hole exists

Answer 1

To find the location of a hole in a function, you need to factor both the numerator and denominator of the rational function and see if there is any common factor that can be canceled out.

Step-by-step explanation:

To find the location of a hole in a function, you need to factor both the numerator and denominator of the rational function and see if there is any common factor that can be canceled out.

In this case, we have a quadratic function in both the numerator and denominator. The numerator is x^2 + 5x + 6, and the denominator is x^2 + 3x + 2.

By factoring both the numerator and denominator, we can see that we have a common factor of x + 2. Canceling out this factor, we get a simplified function of f(x) = x + 3.

Since there is no x-value that makes the denominator equal to zero, there is no hole in the graph of this function. Therefore, the correct answer is d. No hole exists.