2022-07-16

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.

Deacon Nelson

Expert

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).
Thus, only in A is the theorem stated correctly and with the appropriate plausibility.

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