Question

Hey, Its the same person. This is Algebra 2. Please Help!

Answer 1

first option

Explanation:

Given

f(x) =
`(2x^2+5x-12)/(x+4)` ← factorise the numerator

=
`((x + 4)(2x-3))/(x+4)` ← cancel (x + 4) on numerator/ denominator

= 2x - 3

Cancelling (x + 4) creates a discontinuity ( a hole ) at x + 4 = 0, that is

x = - 4

Substitute x = - 4 into the simplified f(x) for y- coordinate

f(- 4) = 2(- 4) - 3 = - 8 - 3 = - 11

The discontinuity occurs at (- 4, - 11 )

To obtain the zero let f(x) = 0, that is

2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
`(3)/(2)`

There is a zero at (
`(3)/(2)`, 0 )

Thus

discontinuity at (- 4, - 11 ), zero at (
`(3)/(2)`, 0 )