What are the discontinuity and zero of the function f(x) = quantity x squared plus 5 x plus 4 end quantity over quantity x plus

Question

3 years ago

14

What are the discontinuity and zero of the function f(x) = quantity x squared plus 5 x plus 4 end quantity over quantity x plus

4?
Discontinuity at (−4, −3), zero at (−1, 0)
Discontinuity at (−4, −3), zero at (1, 0)
Discontinuity at (4, 3), zero at (−1, 0)
Discontinuity at (4, 3), zero at (1, 0)

Mathematics

1 answer:

kap26 [50] · Answer 1 · 2022-01-07T01:28:03+03:00

kap26 [50]3 years ago

4 0

Answer:

Discontinuity at (−4, −3), zero at (−1, 0)

Step-by-step explanation:

The expression simplifies to ...

$\dfrac{x^2+5x+4}{x+4}=\dfrac{(x+4)(x+1)}{(x+4)}=x+1 \qquad\text{$x\ne -4$}$

This is undefined at x=-4, hence there is a discontinuity there, and is zero for x=-1.

There is a discontinuity at x=-4, and a zero at (-1, 0).