What are the discontinuity and zero of the function f(x) = x^2 + 8x + 7 / x + 1

- Discontinuity at (-1,6)

 - The zero is at (-7,0)

Step-by-step explanation:

Given the function , you need to factor the numerator. Find two number whose sum be 8 and whose product be 7. These are 1 and 7, then:

Then, the denominator is zero when

Therefore, does not belong to the Domain of the function. Then, (-1,6) is a discontinuity point.

Simplifying, you get:

You can observe that a linear function is obtained.

This function is  equal to zero when , therefore the zero of the function is at (-7,0).

ANSWER

Discontinuity:

Zero:

EXPLANATION

The given rational function is

We factor function to obtain:

This function is not continuous when

The function is not continuous at

When we simplify the function, we get;

The zero(s) occur at

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step-by-step explanation: