Question

what is the discontinuity of the function f(x)=x^2-3x-28/x+4

Answer 1

When we talk about descontinuity we talk about values the variable "x" cannot take, an indetermination or a "non existence" value.
Looking at the function:
\[f:f(x)=\frac{ x ^{2}-3x-28 }{ x+4 }\]
We know it's a rational function, and in the definitions of existence, the denominator cannot take the value "0" (why?). In the world of mathematics it's not been defined or is unknown the value of a number divided by 0.
So having all that in mind, I ask you:
What value of x makes the denominator equal 0?

Answer 2

7,0 @Owlcoffee

Answer 3

Oh no no... That's incorrect, I'll put it in more simple terms.
When I say the denominator cannot take the value 0, what we would want to to is search or find the value of x that do have does properties.
So we will make the denominator equal zero, in order to find that value x will not take.
\[x+4=0\]
sustracting 4 on both sides:
\[x=-4\]
Now, with the value of x, we've just found is actually the value of x that we can never give the function.

Answer 4

4.-3 or -4 -11

Answer 5

Just -4, because if we give it the value of "-3", "4" , "-11" it'll give us a number, meaning it really DO exist, so that means it has no discontinuity on those values of x.
But if we give it the value of -4, it'll look like this:
\[\frac{ (-4)^{2}-3(-4)-28 }{ (-4)+4 }=\frac{ 16+12-28 }{ 4-4 }=\frac{ 0 }{ 0 }\]
if you put 0/0 in your calculator, it'll say "math error" bevause we don't know what 0/0 is.
So we say that the function is discontinous at the value of -4

Answer 6

i dont have just 4 as an option though

Answer 7

But you put a -4 earlier on...

Answer 8

ik but it has to have a -4 and another number

Answer 9

Then it has to be -4 -11.