Which could be the entire interval over which the function, f(x), is positive?

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02-06-2022
Mathematics

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Which could be the entire interval over which the function, f(x), is positive?

Sagot :

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jimthompson5910 jimthompson5910 · Answer 1 · 2022-06-02T10:09:44-04:00

Answer: Choice B. (-2, 1)

Why?

Notice that f(x) is positive when -2 < x < 1. In other words, f(x) is positive when x = -1 and when x = 1.

This interval of -2 < x < 1 translates directly to the interval notation of (-2, 1)

Unfortunately this interval notation looks identical to ordered pair notation. Be sure not to mix the two concepts up.

The parenthesis in interval notation tell the reader "do not include the endpoints". We cannot include x = -2 nor x = 1 because these values make f(x) zero, but we want f(x) > 0.

Something like choice D is a non-answer because the value x = 2 is in the interval (1,4), but f(2) = -8 which isn't positive. We can rule choice D out because of it. Choices A and C are similar situations.

Sagot :

Answer: Choice B. (-2, 1)

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