Question

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)

Answer 1

Answer:

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

Step-by-step explanation:

The expression simplifies to ...

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

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).