Question

Which is a valid prediction about the continuous function f(x)?
f(x) ≥ 0 over the interval [5, ∞).
f(x) ≤ 0 over the interval [–1, ∞).
f(x) > 0 over the interval (–∞, 1).
f(x) < 0 over the interval (–∞. –1)

Answer 1

Without seeing the graph, it's impossible to tell. The same can be said if we don't know the function rule. However, we can rule out three non-answers. 

Choice B is false because the interval [1,3] has f(x) below zero but the rest of the interval to the right of x = 3 has f(x) not below zero.

Choice C is false. The value x = -1 leads to f(x) = 0 which is not greater than 0

Choice D is false because the values 8 and 4 are positive

After eliminating B, C, & D, we are left with choice A as the answer.

Answer 2

The valid prediction about the continuous function f(x) is option A f(x) ≥ 0 over the interval [5, ∞).

What is a function?

Function is a type of relation, or rule, that maps one input to specific single output.

B. f(x) ≤ 0 over the interval [–1, ∞).

The interval [1,3] has f(x) below zero but the rest of the interval to the right of x = 3 has f(x) not so, option B is false.

C. f(x) > 0 over the interval (–∞, 1).

The value x = -1 leads to f(x) zero which is not greater than 0. Choice C must be false.

D. f(x) < 0 over the interval (–∞. –1)

The values 8 and 4 are positive leads to Choice D false.

Hence, choice A is the answer.

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