State whether the graph has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous.?

Question

State whether the graph f(x) = x^3 - x^2 - 12x / x + 3 has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous.

Thanks so much everyone who answers & happy thanksgiving!

Answer 1

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this a point discontinuity, at x=3 , the limit exists, but this is discontinuous function (undefined at x=3),

keep in mind that:

f(x)=(x-1)/(x-1) does not equal to f(x)=1 , the first is not continuous (undefined at x=1), while the latter is continuous everywhere.

Answer 2

It has a discontinuity at x = -3. I don't know the precise definitions of the various types of discontinuity but infinite seems to be a good description of what happens.

Answer 3

The function is actually continuous/there's not enough information given in the question.

The domain and codomain of the function have not been given. For it to be a function, it needs to be defined at every point in its domain. As the function given is not defined at x=3, the only assumption you can make is that the function has domain R/{3} (ie all real numbers except 3). If that is the case, then it is continuous at every point in its domain, so is a continuous function.

To extend the function to the entire real line, you need to assign a value to f(3). If you assign the value -3, then it is continuous (as that is the limit as x->3), but if you assign a different value it is not, and will have a discontinuity at x=3.

Answer 4

the function is discontinuous

however, since

(x+3)(x -4)x / x+3

= x(x-4)

its limit exists

it is a point discontinuity and can be removed.

but now it is definitely a discontinuous function