Using set notations, we have that:
1. The range of the function is:
- Set-builder: {x | x ≥ -15}
2. The function is increasing on:
3. The function is decreasing on:
4. The function is negative on:
- Inequality: 0.918 < x < 5.082.
- Set-builder: {x | 0.918 < x < 5.082}.
- Interval: (0.918, 5.082).
<h3>What is the standard interval notation?</h3>
The standard interval notation of an interval of lower bound a and upper bound b is given by:
[a,b].
The inequality notation is:
a ≤ x ≤ b
The set builder notation is:
{x | a ≤ x ≤ b}.
<h3>What is the range of the function?</h3>
The range of a function is the set that contains all possible output values for the function. In a graph, it is given by the values of y of the function.
Hence, for this problem, the range is given by these following notations:
- Set-builder: {x | x ≥ -15}
<h3>When is a quadratic function increasing and when it is decreasing?</h3>
Considering a concave up quadratic function, as given in this problem, we have that:
- It decays for the values of x before the vertex.
- It increases for the values of x after the vertex.
In this problem, the vertex is at x = 3, hence the intervals are given as follows:
2. The function is increasing on:
3. The function is decreasing on:
<h3>When a function is negative?</h3>
A function is negative when it's graph is below the x-axis. Hence, for this problem, we have that:
4. The function is negative on:
- Inequality: 0.918 < x < 5.082.
- Set-builder: {x | 0.918 < x < 5.082}.
- Interval: (0.918, 5.082).
More can be learned about set notations at brainly.com/question/24462379
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