An interval is used the describe the behavior of a function as it changes for different input values
The correct option for the true statement regarding the represented function are;
f(x) > 0 over the interval (1, ∞)
f(x) ≤ 0 over the interval (-∞, 1]
The reason the selected statements are correct is as follows:
The values of the points on the given graph from left to right are;
From (-∞, -∞), we have, (-4, -5), (-3, 0), (1, 0), (2, 25) to (∞, ∞)
In the interval notation, we have that;
A square bracket means an include point in an interval, while a round bracket means an excluded point or value
Over the interval (1, ∞), which is from 1 to infinity, where 1 and ∞ are excluded, the y-value, and therefore, f(x) is greater than zero, therefore
- f(x) > 0 over the interval (1, ∞)
Over the interval (-∞, 1), which is from negative infinity to 1, where ∞ is excluded, the y-value, and therefore, f(x) is less than or equal to zero, therefore
- f(x) ≤ 0 over the interval (-∞, 1]
Therefore, the true statements are;
f(x) > 0 over the interval (1, ∞) and f(x) ≤ 0 over the interval (-∞, 1]
Learn more about the interval of a function here:
https://brainly.com/question/12223134
