What is the discontinuity and zero of the function f(x) = the quantity of 2 x squared plus 5 x minus 12, all over x plus 4?

Question

amilapsn · Answer

A function is said to be discontinuous at a point if we can't draw the graph without lifting our pen at that point.

mrnood · Answer

in a function like this the discontinuity will occur where the denominator = 0

$$f(x) = \frac{ 5x ^{2}+5x-12 }{ x+4 }$$

If you set f(x) = 0 then you are left with just the quadratic to solve

mrnood · Answer

CORRECTION - should be 2x^2 above

BUT
2x^2+5x-12  = (x+4)(2x-3)

so the equation becomes y=2x-3

which has no discontinuity.

Have I interpreted the equation correctly?

sweetburger · Answer

Isnt this still a discontinuous function?

mrnood · Answer

if the equation is

$$f(x) = \frac{ (2x)^{2}+5x-12 }{ (x+4) }$$

THEN my comments above are true  because(2x)^2 = 4x^2

@sweetburger 
It looks like it should be - but because the denominator cancels with the factor in the numerator it becomes a continulas straight line

sweetburger · Answer

Yea I realized when I graphed it that you are indeed correct.

sweetburger · Answer

Wait actually according to my graphing calculator there is a large gap in the graph

sweetburger · Answer

ill screenshot it one second

mrnood · Answer

attachment

mrnood · Answer

the question asks for the 'zero' 
but in most cases there are 2 zeroes

I think I may have misinterpreted the way the question is written - or it is written incorrectly.

sweetburger · Answer

welp i was doing 5x^2 instead of 2x^2 my bad

mrnood · Answer

soz - that was my initial typo

but there are 2 zeroes in other values for ax^2

sweetburger · Answer

Yea, I see the 2 zeroe values with the correct equation. I understand where your answer came from now.

mrnood · Answer

no - my point is that if the equation is as I wrote then there is ONE zero (as it is a straight line - but NO discontinuity

If the equation is other, then there are 2 zeroes , and a discontinuity @ x=-4

sweetburger · Answer

I mean I see where your coming from as the x+4 cancel out and your left with a straight line with no discontinuities represented by y=2x+3. At least i think this is what your were saying.

mrnood · Answer

yes - that's it

I still think there is an error with the question, or with my interpretation.

But the asker is offline so I'll wait foe his reply.

sweetburger · Answer

Yea the question seems to be misworded in some way or the asker typed it in wrong.