Question

Which of the following is guaranteed by the Intermediate Value Theorem, iffis a continuous function on the closed interval [-13, -5) where f(-13) = 4 and f(-5) = 11

a.f(c) = -7 for at least one c in the open interval (4, 11)
b.f(c) = 7 for at least one c in the open interval (-13,-5)
c.f(c) = -7 for at least one c in the open interval (-13,-5)
d.f(c) = 7 for at least one cin the open interval (4,11)

Answer 1

The Intermediate Value Theorem guarantees that for a continuous function on [-13, -5) with f(-13) = 4 and f(-5) = 11, there will be a value c in the interval (-13, -5) such that f(c) = 7. Option b

Step-by-step explanation:

The Intermediate Value Theorem (IVT) states that for any value between f(-13) and f(-5) there is at least one number c in the interval (-13, -5) such that f(c) equals that value, since f is continuous on [-13, -5). Given that f(-13) = 4 and f(-5) = 11, the IVT guarantees a value f(c) = 7 for some c in the interval (-13, -5).

None of the other options are supported by the IVT in the given interval since they either do not lie between the range of f(-13) and f(-5) or fall outside of the specified domain of the function. option b