Question

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Answer 1

The largest interval in which the function is continuous is given by:

(-∞, -3).

What is the continuity concept?

A function f(x) is continuous at x = a if it is defined at x = a, and:

$\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)$

A function is also not continuous for the values of x which are outside the domain of the function, hence a fraction is not continuous at the zeroes of the denominator.

In this problem, the zeroes of the denominator of the function are:

x = -3, x = 4.

Hence the continuity intervals are:

• (-∞, -3).

• (3,4).

• (4,∞).

The largest one is the first, as |-3| < |4|, meaning that it is a larger distance from infinity.

More can be learned about the continuity of a function at brainly.com/question/24637240

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