# Calculus

posted by Maura

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

1. Reiny

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)

## Similar Questions

1. ### Calculus

consider k(t)=(e^t)/(e^t-7) on[-7,7] Is this function continuous on the given interval?
2. ### AP Calculus

a continuous function f has domain (1,25) and range (3,30). if f'(x) is less than 0 for all x between 1 and 25, what is f(25)?
3. ### math

Use a graph to determine whether the given function is continuous on its domain. HINT [See Example 1.] f(x) = x + 7 if x < 0 2x − 5 if x ≥ 0 1 continuous discontinuous If it is not continuous on its domain, list the …
4. ### MATH

A continuous function, f, has domain all real numbers. If f(-1) = 5 and f(1) = -5, explain why f must have at least one zero in the interval [-1, 1].
5. ### MATH

A continuous function, f, has domain all real numbers. If f(-1) = 5 and f(1) = -5, explain why f must have at least one zero in the interval [-1, 1].
6. ### algebra

2. The function f is defined as follows f(x)={4+2x if x<0 {x^2 if x>0 a) Find the domain of the function b) Locate any intercepts c) Graph function d) Based on graph find range e) Is f continuous on its domain?
7. ### Calculus

Find all values of a, B so that the function f(x)=1 if x>3, f(x)=ax-10 if x<3, and f(x)=B otherwise is continuous everywhere. I think a is continuous everywhere since ax-10 is a polynomial, and b is continuous at x=3.
8. ### Calculus

True or False,... Im confused If the continuous function f(x) has a domain (-∞, +∞), then either lim --> ∞ exists, or limit X--> ∞ is +-∞
9. ### Math

A continuous function f has domain of all real numbers. If f(-1) = 5 and f(1) = -5, explain why function f must have at least one zero in the interval [-1, 1]
10. ### Math

You are packing books into a box. The box can hold at most 10 books. The function y=5.2x represents the weight y (in pounds) of x books. a. Is 52 in the range?

More Similar Questions