Let's analyze the graph to answer the questions. Here's a breakdown based on the image:

1. Domain:

The domain is the set of all possible $x$-values for which the function $f(x)$ is defined. From the graph, the function starts at $x = -10$ and ends at $x = 10$.

Domain: $[-10, 10]$

2. Range:

The range is the set of all possible $y$-values. From the graph:

• The minimum $y$-value appears to be $-10$ (at $x = 5$).
• The maximum $y$-value is $9$ (between $x = -7$ and $x = -5$).

Range: $[-10, 9]$

3. Strictly Increasing:

A function is strictly increasing on an interval if, as $x$ increases, $f(x)$ also increases. Observing the graph:

• The function is increasing from $x = -10$ to $x = -5$.

Strictly Increasing: $(-10, -5)$

4. Strictly Decreasing:

A function is strictly decreasing on an interval if, as $x$ increases, $f(x)$ decreases. From the graph:

• The function decreases from $x = -5$ to $x = 2$.

Strictly Decreasing: $(-5, 2)$

5. Constant:

A function is constant on an interval if $f(x)$ remains the same as $x$ varies. From the graph:

• There are no intervals where the function is strictly constant.

Constant: NONE

6. Local Maxima:

Local maxima are points where $f(x)$ changes from increasing to decreasing. In the graph:

• The local maximum occurs at $x = -5$, where the $y$-value is $9$.

Local Maxima: 9

7. Local Minima:

Local minima are points where $f(x)$ changes from decreasing to increasing. In the graph:

• The local minimum occurs at $x = 2$, where the $y$-value is $-10$.

Local Minima: $-10$

Would you like further details on any of these answers, or do you have more questions?

Additional Questions

1. What is the slope of the graph in the interval where it is increasing?
2. Can you identify the coordinates of the inflection points on this graph?
3. Is the function continuous over its entire domain?
4. How would the intervals change if the endpoints were included in the increasing or decreasing sets?
5. What is the average rate of change of the function from $x = -10$ to $x = 10$?

Tip:

When writing the domain and range in interval notation, use square brackets $[ ]$ to indicate that the endpoints are included and parentheses $( )$ when they are not.