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Explain, using the theorems, why the function is continuous at every number in its domain. Q(x) = 3 x − 9 x3 − 9 Q(x) is a polynomial, so it is continuous at every number in its domain. Q(x) is a rational function, so it is continuous at every number in its domain. Q(x) is built up from functions that are continuous for all real numbers, so it is continuous at every number in its domain. Q(x) is not continuous at every number in its domain. none of these

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jolis1796

Answer:

Q(x) is a polynomial, so it is continuous at every number in its domain.

Step-by-step explanation:

All polynomial functions are continuous everywhere.

Continuity at a Point.

Let f be defined on an open interval containing c. We say that f is continuous at c if

lim (x→c) f(x) = f(c)

This indicates three things:

1. The function is defined at x = c.

2. The limit exists at x = c.

3. The limit at x = c needs to be exactly the value of the function at x = c

For the example,

lim (x→c) f(x) = f(c) = 3*(c) − 9*(c)³ − 9

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