Question

I need help doing everything.

Answer 1

Using set notations, we have that:

1. The range of the function is:

• Inequality: x ≥ -15.

• Set-builder: {x | x ≥ -15}

• Interval: [-15, ∞).

2. The function is increasing on:

• Inequality: x > 3.

• Set-builder: {x | x > 3}

• Interval: (3, ∞).

3. The function is decreasing on:

• Inequality: x < 3

• Set-builder: {x | x < 3}

• Interval: (-∞, 3).

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).

What is the standard interval notation?

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}.

What is the range of the function?

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:

• Inequality: x ≥ -15.

• Set-builder: {x | x ≥ -15}

• Interval: [-15, ∞).

When is a quadratic function increasing and when it is decreasing?

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:

• Inequality: x > 3.

• Set-builder: {x | x > 3}

• Interval: (3, ∞).

3. The function is decreasing on:

• Inequality: x < 3

• Set-builder: {x | x < 3}

• Interval: (-∞, 3).

When a function is negative?

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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