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Predict which statements are true about the intervals of the continuous function. Check all that apply.

f(x) > 0 over the interval (−, 3).
f(x) ≤ 0 over the interval [0, 2].
f(x) < 0 over the interval (−1, 1).
f(x) > 0 over the interval (–2, 0).
f(x) ≥ 0 over the interval [2, ).

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The statements that are true about the intervals of the continuous function are:

  • f(x) ≤ 0 over the interval [0, 2]. (Option B)
  • f(x) > 0 over the interval (–2, 0). (Option D)
  • f(x) ≥ 0 over the interval [2, ) (option E)

What is a continuous function?

If a continuous function is defined differently at distinct intervals, it is said to be a piecewise continuous function.

What is the proof of the above?

(a) f(x) > 0 over the interval (, 3).

Using the table of f(x), the values in (, 3) are values less than 3; i.e. -3 to 2. If f(2) = 0, then f(x) > 0 is not true

(b) f(x) ≤ 0 over the interval [0, 2].

The values in [0, 2] are values from 0 to 2; i.e. 0, 1 and 2.

If f(0) = 0, f(1) = -3 and f(2) = 0

Then, f(x) ≤ 0

(c) f(x) < 0 over the interval (−1, 1).

Using the table of f(x), the values in (-1, 1) are values between -1 and 1; i.e. 0

If f(0) = 0, then f(x) < 0 is not true

(d) f(x) > 0 over the interval (–2, 0).

Using the table of f(x), the values in (-2, 0) are values between -2 and 0; i.e. -1

If f(-1) = 3, then f(x) > 0 is true

(e) f(x) ≥ 0 over the interval [2, )

Using the table of f(x), the values in [2, ) are values from 2; i.e. 2 and 3

If f(2) = 0 and f(3) = 15, then f(x) ≥ 0  is true

Therefore, only Options B, D, and E are correct.

Learn more about continuous functions at:
https://brainly.com/question/18102431

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