Question

Can someone help me answer this?

Given the function f(x)= x^2+7x+10 / x^2+9x+20
Describe where the function has a hole and how you found your answer.

We need to simplify the function by factoring the numerator and the denominator. Plug the excluded values into the simplified function to find the hole.

Answer 1

Explanation:

Factor the given function:

(x + 2)(x + 5)

f(x) = --------------------

(x + 5)(x + 4)

The factor (x + 5) can be crossed out in numerator and denominator. There is a 'hole' at x = -5 (which comes from setting (x + 5) = 0 and solving for x).

If we do cancel the (x + 5) factors, we are left with

(x + 2)

f(x) = ------------- . We can't just substitute x = -5 because the original

(x + 4) function is not defined for that x value. However, we

can locate the hole by letting x have the value of a litle more than -5, obtaining:

( -5+ + 2)

f(-5+) = -------------, which comes out to approx. -3/-1, or +3 .

(-5+ + 4)

So the hole location is (-5, 3).

f(x) = --------------------

(x + 5)(x + 4)