Question

x | f(x)
-5 | 8
-3 | 4
-1 | 0
1 | -2
3 | -2
5 | 0
7 | 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).

Explanation:

Check each option:

• For [5, ∞): f(5)=0 and f(7)=4>0; no negative values in given data here, so valid.
• For [-1, ∞): f(1)=-2<0 contradicts f(x)≤0? No, wait f(-1)=0, f(1)=-2, but the option says ≤0 which is true? Wait no—wait f(7)=4>0, so [-1,∞) has f(7)=4>0 which violates ≤0.
• For (-∞,1): f(-5)=8>0, f(-3)=4>0, f(-1)=0, f(1)=-2; but 0 is not >0, so invalid.
• For (-∞,-1): f(-5)=8>0 contradicts <0.

Only the first option holds.

Answer:

f(x) ≥ 0 over the interval [5, ∞).