A2-column table with 7 rows. the first column is labeled x with entries negative 5, negative 3, negative 1, 1, 3, 5, 7. the second column is labeled f of x with entries 8, 4, 0, negative 2, negative 2, 0, 4.
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).

f(x) ≥ 0 over the interval [5, ∞). is a valid prediction.

Step-by-step explanation:

We graph the points in the table and analyze the graph that results.

The graph is attached.

With the graph in hand, let us evaluate each of the choices given.

f(x) ≥ 0 over the interval [5, ∞).

The function is positive for x  ≥ 0; therefore this looks like a valid prediction.

f(x) ≤ 0 over the interval [–1, ∞).

f(x) ≤ 0 only over the interval [-1,5}; therefore this choice not a valid prediction.

f(x) > 0 over the interval (–∞, 1).

f(x) > 0 over the interval (5, ∞]: this choice is not a valid prediction.

f(x) < 0 over the interval (–∞. –1).

f(x) < 0 over the interval [-1, 5]: this choice is also not a valid prediction.

Thus only 1st choice is correct: f(x) ≥ 0 over the interval [5, ∞).

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