Homework Help: Calculus

Posted by Maura on Tuesday, February 5, 2013 at 10:54pm.

Explain, using the theorems, why the function is continuous at every number in its domain.

F(x)= 2x^2-x-3 / x^2 +9

A) F(x) is a polynomial, so it is continuous at every number in its domain.
B) F(x) is a rational function, so it is continuous at every number in its domain.
C) F(x) is a composition of functions that are continuous for all real numbers, so it is continuous at every number in its domain.
D) F(x) is not continuous at every number in its domain.
E) none of these

State the domain. (Enter your answer using interval notation.)

Calculus - Reiny, Tuesday, February 5, 2013 at 11:45pm
The numerator is defined for every value of x you choose,
the denominator is always positive, so there is no danger of us dividing by zero, which would have caused a discontinuity.
so continuous for all values of x

B)

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