The image shows a graphing tool with a plotted function in orange. The graph is set against a grid with an x-axis ranging from -4 to 4 and a y-axis ranging from -30 to 20. There are two distinct peaks and two troughs on the curve.

Question

The task is to find the local minimum and maximum values for the given function over specified intervals:

Over the interval ([-3, -1]), the local minimum is __________.
Over the interval ([-1, 0]), the local maximum is __________.
Over the interval ([0, 3]), the local minimum is __________.

Answer 1

To determine the local minimum and maximum values for the plotted function over the specified intervals, we will analyze each interval based on the characteristics described in your prompt.

1. Over the interval ([-3, -1]):

   • In this interval, we are looking for local minimums. Since it contains two distinct peaks, the minimum will likely be found at either boundary or at a point in between where the function dips down to its lowest point.
   • Based on typical behavior, if the curve has a trough between these values, that will be the local minimum.

   Local minimum is at y = [specific value determined from graph].

2. Over the interval ([-1, 0]):

   • In this interval, we need to locate a local maximum. Given that this range continues from an interval that may contain a peak, the maximum should occur near the peak towards the right side of the range.

   Local maximum is at y = [specific value determined from graph].

3. Over the interval ([0, 3]):

   • Again, we are searching for a local minimum. This interval may lead to the second trough, especially if the curve dips downwards before hitting the peak or another downward sloping section.

   Local minimum is at y = [specific value determined from graph].

For precise numerical values, graphical inspection or mathematical calculations at critical points derived from a given function would be required.

Please, refer to the graph values to fill in the specific values for the local minimum and maximum.

Answer 2

Over the interval [–3, –1], the local minimum is???? what is the options -2 -1 or 0

Over the interval [–1, 0], the local maximum is what is the options -1 4.39 or 0

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

✔ –32

Answer 3

To complete the statements based on the options provided:

1. Over the interval [-3, -1], the local minimum is -2. (It is likely the lowest value in that range based on the provided options).

2. Over the interval [-1, 0], the local maximum is 4.39. (This indicates it is the highest value in the specified range based on the options).

3. Over the interval [0, 3], the local minimum is -32. (You already provided this value, and it is confirmed).

So, filling in the blanks we have:

• Over the interval ([-3, -1]), the local minimum is -2.
• Over the interval ([-1, 0]), the local maximum is 4.39.
• Over the interval ([0, 3]), the local minimum is -32.

Answer 4

Over the interval [–3, –1], the local minimum is

✔ 0

On a coordinate plane, a curved line with a minimum value of (negative 1, negative 2), crosses the x-axis at (negative 2, 0) and the y-axis at (0, 0).
Determine the x-intercepts of the function. Check all that apply.

(–2, 0)
(–1, –2)
(0, 0)
(1, 0)
(2, 0)

Answer 5

Given the description of the function and its characteristics, we can determine the x-intercepts (where the graph crosses the x-axis, meaning \(y = 0\)).

From the provided details:

1. The function crosses the x-axis at \((-2, 0)\).
2. The function also crosses the y-axis at \((0, 0)\).

The options provided are:

• (–2, 0)
• (–1, –2)
• (0, 0)
• (1, 0)
• (2, 0)

Checking each option:

1. (–2, 0) - This is indeed an x-intercept since the y-value is 0 (the function crosses the x-axis here).
2. (–1, –2) - This is not an x-intercept; it is a point on the curve where \(y \neq 0\).
3. (0, 0) - This is also an x-intercept, as it indicates the function crosses the x-axis at the origin.
4. (1, 0) - This point is not mentioned in the description, so it is not an x-intercept based on the information given.
5. (2, 0) - Similar to (1, 0), this point is not listed in the description and is not an x-intercept.

Conclusion:

The x-intercepts of the function are:

• (–2, 0)
• (0, 0)

So the correct answers are (–2, 0) and (0, 0).