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

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

Explanation:

Answer 2

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

Explanation:

The expression simplifies to ...

`(x^2+5x+4)/(x+4)=((x+4)(x+1))/((x+4))=x+1 \qquad\text{$x\\e -4$}`

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).