Intermediate Value Theorem

Question

Suppose that  𝑓(𝑥)  is a continuous function, whose domain is the interval  [−2,2] .

If  𝑓(−2)⋅𝑓(2)<0f(−2)⋅f(2)<0 , we may conclude, from the Intermediate Value Theorem, that...

Group of answer choices

1. 𝑓(0)=0
2. 𝑓(𝑥) is never zero.
3. 𝑓(𝑥) is zero for some  𝑥  in  [−2,2] .
4. 𝑓(𝑥) is zero for all  𝑥's in  [−2,2].
5. 𝑓(𝑥) is an odd function.

Answer 1

Since f(-2) • f(2) < 0, f(-2) and f(2) have opposite signs.

This fact combined with the fact that f(x) is continuous on [2,2] tells us that f(x) = 0 for at least one number x between -2 and 2.