Question

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

Answer 1

Answer:

the answer is:

b

d

e

Answer 2

Functions are used to show relationships between variables. The true statements are:

• f(x) ≤ 0 over the interval [0, 2].
• f(x) > 0 over the interval (–2, 0).
• f(x) ≥ 0 over the interval [2, $\infty$)

I've added as an attachment, the table of values of f(x)

Next, we test the given options

(a) f(x) > 0 over the interval ($-\infty$, 3).

Using the table of f(x), the values in ($-\infty$, 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, $\infty$)

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

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

Hence, the true statements are:

• f(x) ≤ 0 over the interval [0, 2].
• f(x) > 0 over the interval (–2, 0).
• f(x) ≥ 0 over the interval [2, $\infty$)

Read more about functions over interval at:

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