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)…

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).

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).

Answer

Explanation:

Step1: Analyze the given data points

We have points (-5, 8), (-3, 4), (-1, 0), (1, -2), (3, -2), (5, 0), (7, 4).

Step2: Check each option

  • Option 1: For (x\in[5,\infty)), when (x = 5), (f(5)=0) and when (x = 7), (f(7)=4>0). Since the function is continuous, (f(x)\geq0) over the interval ([5,\infty)).
  • Option 2: When (x = 7> - 1), (f(7)=4>0), so (f(x)\leq0) over the interval ([-1,\infty)) is false.
  • Option 3: When (x=-1), (f(-1) = 0), so (f(x)>0) over the interval ((-\infty,1)) is false.
  • Option 4: When (x=-5), (f(-5)=8>0), so (f(x)<0) over the interval ((-\infty,-1)) is false.

Answer:

(f(x)\geq0) over the interval ([5,\infty))