Calculus

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.)

asked by Maura
  1. 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)

    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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
  2. 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]
  3. 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? a) The domain
  4. 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? Explain. b. Is 15 in the domain? Explain. C. Is the domain discrete or
  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. 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].
  7. 11th grade maths

    A.give an example of a function whose domain is {3,4,7,9}? and whose range is {-1,0,3} B.Find two different functions whose domain is {3,8}and whose range is {-4,1} C Explain why there does not exist a function whose domain is
  8. Math (Calc.)

    1.Use the IVT to explain why the following is true. If f continuous on (a,b) and f(x) does not equal to zero for all x in the interval (a,b), then f(x) > for all x in the interval (a,b) or f(x) < 0 for all x in the interval
  9. math111(3)

    The function f(x)=(x+6)^2 is not one-to-one. Choose the largest possible domain containing the number 0 so that f(x) restricted to this domain is one-to-one. The largest possible domain is [-6,infinity) If the restriction function
  10. Need help asap

    I need help! Reasoning: Can a function have an infinite number of values in its domain and only a finite number of values in its range? If so, describe a real-world situation that could be modeled by such a function. Writing: What

More Similar Questions