Question

The function f(x) is continous on the interval (-3, 4). If we know that f(-1) = 4 and f(3) = 7, what can we say about the outputs of f(x), i.e. what values does f definitely take and/or not take?

Answer 1

Answer:

f definitely takes all the values between 4 and 7.

Step-by-step explanation:

From the data that is given to us, we know that f(x) is continuous on the interval (-3,4). Both values -1 and 3 are inside this interval, so therefore we can say that the function f(x) is continuous on the interval [-1, 3].

The definition of continuous function on an interval [x, y] tells us that the function takes all the values between f(x) and f(y).

Therefore, we can say that f definitely takes all the values between 4 and 7. (f(-1) and f(3))