A 2-column table with 7 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries 15, 0, 3, 0, negative 3, 0, 15. 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 (–2, 0). f(x) ≥ 0 over the interval [2, ).

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itzzsarita itzzsarita · Answer 1 · 2021-02-03T21:11:56+01:00

Answer:

2nd, 4th, 5th

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lisboa lisboa · Answer 2 · 2021-09-08T05:46:35+02:00

Options 2, 4 and 5 are correct.

The intervals that satisfies the condition are

f(x)<=0 over the interval [0,2]

f(x)>0 over the interval (-2,0)

f(x)>=0 over the interval [2,∞)

Given : The table with x and f(x) values

Lets analyze the table and check the each option that satisfies f(x) or not .

Look the values of x that is from -3 to 3, the f(x) values are both positive and negative . So f(x)>0 is false over the interval (-∞,3)

From the interval 0 to 2, the f(x) values are 0 and negative .

So , f(x)<=0 over the interval [0,2]

Over the interval (-1,1), f(x) values are both positive and negative

So, f(x)<0 is false over the interval (-1,1)

In the interval (-2,0) , the f(x) is positive.

So , f(x)>0 over the interval (-2,0)

In the interval [2,∞), f(x) is positive

So , f(x)>=0 over the interval [2,∞)

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