Explain in your own words what the Intermediate Value Theorem says and why it se

Question

Explain in your own words what the Intermediate Value Theorem says and why it seems plausible.

.A.

The Intermediate Value Theorem states that for a continuous function f(x) over the closed interval [a,b], f(x) takes on every value between f(a) and f(b). This seems plausible because if the function did not take on every value between f(a) and f(b), there would be a value for f(x) that did not exist, and thus the function would not be continuous.

B

The Intermediate Value Theorem states that for every value of x between a and b in f(x), if f(a) exists, then f(b) must exist if b is in the domain. This seems plausible because if the function did not take on every value between f(a) and f(b), there would be a value for f(x) that did not exist, and thus the function would not be continuous.

C.

The Intermediate Value Theorem states that for a continuous function f(x) over the closed interval [a,b], f(x) takes on every value between f(a) and f(b). This seems plausible because if b is in the domain of x, then f(b) must exist.

D.

The Intermediate Value Theorem states that for every value of x between a and b in f(x), if f(a) exists, then f(b) must exist if b is in the domain. This seems plausible because if b is in the domain of x, then f(b) must exist.

Explanation / Answer

option A is correct.

As it states that the function f(x) is continuous.

In B and C it is not stated that f(x) is continuous.

In D it states f(x) is continuous but do not state that it assumes every values in between f(a) and f(a).

So only in A it states the theorem correctly with correct plausibility.

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