Question

Find any points of discontinuity for the rational function: y = (x−6)(x+2)(x+5)/(x−9)(x+4)
(1 point)
Responses


x=4, x=−9


x=−4, x=9


x=−2, x=6, x=−5

x=2, x=−6, x=5

Answer 1

To find the points of discontinuity for the rational function

\[
y = \frac{(x−6)(x+2)(x+5)}{(x−9)(x+4)}
\]

we need to determine where the function is undefined. A rational function is typically undefined wherever the denominator is equal to zero.

Let's set the denominator equal to zero and solve:

\[
(x−9)(x+4) = 0
\]

This gives us two points where the function is discontinuous:

1. \( x - 9 = 0 \) → \( x = 9 \)
2. \( x + 4 = 0 \) → \( x = -4 \)

Thus, the points of discontinuity for the given rational function are:

- \( x = 9 \)
- \( x = -4 \)

So, the correct answer from the options provided is:

**x = −4, x = 9**.