Question

the function f(x) is continuous on its domain of [-9,9] and is plotted below such that the portion of the graph on the interval (-3,2) is hidden from view. given that f(-3) = 3 and f(2) = 5, determine what conclusions can be drawn based on the intermediate value theorem on the interval (-3,2)

Answer 1

The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b] and takes on two values, say c and d, then it must also take on all values between c and d. In this case, we have a function f(x) that is continuous on the interval [-9,9], and we know that f(-3) = 3 and f(2) = 5. Since the portion of the graph on the interval (-3,2) is hidden from view, we can use the Intermediate Value Theorem to conclude that there must be a value of x between -3 and 2 where f(x) takes on any value between 3 and 5.

Step-by-step explanation:

The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b] and takes on two values, say c and d, then it must also take on all values between c and d. In this case, we have a function f(x) that is continuous on the interval [-9,9], and we know that f(-3) = 3 and f(2) = 5. Since the portion of the graph on the interval (-3,2) is hidden from view, we can use the Intermediate Value Theorem to conclude that there must be a value of x between -3 and 2 where f(x) takes on any value between 3 and 5.