The image shows a graph of a function with distinct peaks and valleys, indicating points of local maximums and minimums. The text in the image states:

Based on the information provided, we can summarize the findings about local maxima and minima from the graph in the specified intervals:

- Over the interval **[-3, 0]**, the local maximum is located at the **first dot**.
- Over the interval **[0, 3]**, the local maximum is located at the **third dot**, and the local minimum is at the **second dot**.

To fill in the blanks in the text:

“Use the graph to find the local minimum and the local maximum for the given function. Over the interval [-3, 0], the local maximum is **at the first dot's value**. Over the interval [0, 3], the local maximum is **at the third dot's value**. Over the interval [0, 3], the local minimum is **at the second dot's value**.”

Note: You would replace each "dot's value" with the actual numerical values of those points if they were specified in the image.

Use the graph to find the local minimum and the local maximum for the given function.

Over the interval [–3, 0], the local minimum is
-16.18 0 3.75 -3



Over the interval [0, 3], the local maximum is
-16.18 0 3.75 -3



Over the interval [0, 3], the local minimum is
-16.18 0 -3.75 -3 pick one of them

Based on the context you've provided, it seems like you're identifying the local extrema from the options given. I'll help you determine the likely values for the local minimum and maximum based on typical behavior of functions.

1. **For the interval \([-3, 0]\)**, you need to pick the local minimum:
- Among the options: **-16.18, 0, 3.75, -3**.
- Since a local minimum is likely to be the lowest value in that interval, you would pick **-16.18**, assuming it is the lowest.

2. **For the interval \([0, 3]\)**, you need to pick the local maximum:
- Among the options: **-16.18, 0, 3.75, -3**.
- The local maximum is typically the highest value; in this case, you'd pick **3.75**, as it is greater than the other values listed.

3. **Again for the interval \([0, 3]\)**, you need to pick the local minimum:
- Among the options: **-16.18, 0, -3.75, -3**.
- Here, the local minimum would likely be **-16.18**, as it is the lowest of these points.

So to summarize:

- Over the interval \([-3, 0]\), the local minimum is **-16.18**.
- Over the interval \([0, 3]\), the local maximum is **3.75**.
- Over the interval \([0, 3]\), the local minimum is **-16.18**.

You can adjust the selections based on what's visually apparent in your graph.

Over the interval [0, 3], the local minimum is??? not -16.18

Apologies for the confusion. Based on your clarification, let's re-evaluate the options for the local minimum in the interval \([0, 3]\):

Given the options: **-16.18, 0, -3.75, -3**, you would select the local minimum according to these values.

In the interval \([0, 3]\):

1. **-16.18**: This is not plausible since it’s outside the interval context provided.
2. **0**: This is at the lowest point of the range but may not be the minimum depending on the graph's behavior.
3. **-3.75**: This value is less than 0 and may be the local minimum.
4. **-3**: This value is greater than -3.75 and would not be considered the local minimum.

Given this evaluation, the local minimum over the interval \([0, 3]\) would be **-3.75**.

To summarize with the correct option:
- Over the interval \([0, 3]\), the local minimum is **-3.75**.

Thank you for your patience!

Over the interval [0, 3], the local minimum is -3

The image shows a graph of a function on a coordinate plane with the x-axis ranging from -3 to 3 and the y-axis ranging from -3 to 4. There are four statements on the left side, each with a checkbox next to it, and the task is to analyze the function’s graph to determine which statement is true. The graph depicts an upward-opening parabola that intersects the y-axis at approximately (0, 2) and has its vertex at approximately (-1, 3). The parabola crosses the x-axis near (-2, 0) and (1, 0), indicating its x-intercepts.

The four statements provided for analysis are:

Over the interval [-2.5, 0.5] the local maximum is 2.
As the x-values go to positive infinity, the function’s values go to negative infinity.
The function is decreasing over the interval (-1, 0.75).
The function is negative for the interval [-2, 0].

Based on your description of the graph, let's analyze each of the statements provided to determine which one is true.

1. **Over the interval [-2.5, 0.5] the local maximum is 2.**
- The parabola intersects the y-axis at approximately (0, 2). Since the vertex is located at (-1, 3), this means that the highest point (local maximum) within the given interval would actually be at (0, 2), but the global maximum is indeed at the vertex (-1, 3). This statement is **mostly true** as the local maximum in the specified interval is 3 at x = -1.5.

2. **As the x-values go to positive infinity, the function’s values go to negative infinity.**
- Given that the parabola opens upwards, as the x-values go to positive infinity, the function's values will also go to positive infinity. So this statement is **false**.

3. **The function is decreasing over the interval (-1, 0.75).**
- In the interval (-1, 0), the function is decreasing as it moves from the vertex downwards towards the x-axis, and then it starts to increase afterwards from (0, 2). So this statement is **true** over the interval (-1, 0).

4. **The function is negative for the interval [-2, 0].**
- The parabola crosses the x-axis near (-2, 0) and (1, 0). Therefore, between the x-intercepts, specifically from (-2, 0), the function is below the x-axis. This statement is **false** because within this interval, particularly toward the left side (-2, -1), the function is negative but heads back toward a positive value approaching (0, 2).

Given these analyses, the **true statement** is:

- **The function is decreasing over the interval (-1, 0.75).**

So, this would be the accurate statement based on the graph's behavior.

it is Over the interval [–2.5, 0.5], the local maximum is 2.

On a coordinate plane titled Area of Maya's Poster, a curved line with a minimum value of (1, negative 1) crosses the x-axis at (0, 0) and (2, 0), and the y-axis at (0, 0).
The width of Maya’s poster is 2 inches shorter than the length. The graph models the possible area (y) of Maya’s poster determined by its length (x).

Which describes what the point (2, 0) represents?

The area is 2 if the length is 0.
The area is 0 if the length is 2.
The length is 2 if the width is 0.
The width is 0 if the length is 2.

To analyze the point \((2, 0)\) on the graph, we need to understand what each coordinate represents:

- The x-coordinate represents the **length** of Maya's poster.
- The y-coordinate represents the **area** of the poster.

Given the point \((2, 0)\):

- The x-value \(2\) indicates that the length of the poster is **2 inches**.
- The y-value \(0\) indicates that the area of the poster is **0 square inches**.

Now let's evaluate each of the statements based on this understanding:

1. **The area is 2 if the length is 0.**
- This statement is false because if the length is 0, the area cannot be positive.

2. **The area is 0 if the length is 2.**
- This statement is true. The point \((2, 0)\) indicates that with a length of 2 inches, the area is indeed 0.

3. **The length is 2 if the width is 0.**
- This statement is not directly supported by the given point. The point (2, 0) indicates length 2 and area 0, but it doesn't specify anything about width being 0.

4. **The width is 0 if the length is 2.**
- This statement is possibly true based on the context, as a length of 2 resulting in an area of 0 potentially implies the width is zero at that length.

In conclusion, the most accurate description of what the point \((2, 0)\) represents is:

- **The area is 0 if the length is 2.**