<h2>
Answer:</h2>
The valid prediction about the continuous function f(x) is:
f(x) ≥ 0 over the interval [5, ∞).
<h2>
Step-by-step explanation:</h2>
The table for f(x) is given by:
x f(x)
-5 8
-3 4
-1 0
1 -2
3 -2
5 0
7 4
From the table of values of the function f(x) we see that the value of the function f(x) first decreases and then attains it minimum ( i.e. -2) and then increases continuously after x=5.
Hence, the correct answer is:
f(x) ≥ 0 over the interval [5, ∞).
(
- f(x) ≤ 0 over the interval [–1, ∞).
This option is incorrect since the value of the function at x=5 is greater than zero.
- f(x) > 0 over the interval (–∞, 1).
At x= =-1 we have f(x)=0 .
Hence, the option is incorrect.
- f(x) < 0 over the interval (–∞. –1).
At x= -5 the value of f(x) is greater than zero.
Hence, this option is incorrect )
