Which function is negative for the interval [–1, 1]?

Question

On a coordinate plane, a curved line with a minimum value of (negative 1, negative 2), crosses the x-axis at (negative 2.5, 0) and (0.5, 0), and the y-axis at (0, negative 1).

On a coordinate plane, a curved line with a minimum value of (0, negative 2), crosses the x-axis at (negative 1.5, 0) and (1.5, 0).

On a coordinate plane, a curved line with a maximum value of (0, 2) and a minimum value of (1.5, negative 2.75), crosses the x-axis at (negative 0.6, 0) and (0.6, 0).

On a coordinate plane, a curved line with a maximum value of (negative 1.25, 4) and a minimum value of (1.5, negative 3.5), crosses the x-axis at (negative 1.75, 0), (0.75, 0), and (1.75, 0), and crosses the y-axis at (0, 2).

Answer 1

To determine which function is negative for the interval \([-1, 1]\), we can analyze the information provided for each of the three functions.

1. First Function:

   • Minimum at \((-1, -2)\)
   • Crosses x-axis at \((-2.5, 0)\) and \((0.5, 0)\)
   • Crosses y-axis at \((0, -1)\)

   Within the interval \([-1, 1]\), the function has a minimum value at \((-1, -2)\), which is negative. It crosses the x-axis at \((0.5, 0)\), meaning that it is negative up to \(0.5\). Therefore, this function is negative for the entire interval \([-1, 1]\).

2. Second Function:

   • Minimum at \((0, -2)\)
   • Crosses x-axis at \((-1.5, 0)\) and \((1.5, 0)\)

   In this case, the function is negative at \(x = 0\) (where it has its minimum value of \(-2\)) and crosses the x-axis at \(-1.5\) and \(1.5\). Therefore, it stays negative on the interval \([-1, 1]\) as well.

3. Third Function:

   • Maximum at \((0, 2)\)
   • Minimum at \((1.5, -2.75)\)
   • Crosses x-axis at \((-0.6, 0)\) and \((0.6, 0)\)

   This function has a maximum of \(2\) at \(x=0\), which is positive, and crosses the x-axis at points that suggest it is positive at \(x=0\). Therefore, this function cannot be negative over the interval \([-1, 1]\).

4. Fourth Function:

   • Maximum at \((-1.25, 4)\)
   • Minimum at \((1.5, -3.5)\)
   • Crosses x-axis at points including \((-1.75, 0)\), and \( (0.75, 0)\)

   Since the function has a maximum of \(4\) at \((-1.25)\) and it crosses the x-axis before and after \(1\), the function can turn positive within the interval \([-1, 1]\).

Conclusion:

From this analysis, both the first function and the second function are negative over the interval \([-1, 1]\). However, considering we need to identify only one function accurate with its minimum, the first function is confirmed to be negative throughout the entire interval [−1, 1].

Answer 2

guys you see the U shape? theres one more to the left one more middle and its the middle one

On a coordinate plane, a curved line crosses the x-axis at (negative 1, 0) and the y-axis at (0, 2).
Determine the intercepts.

x-intercept =

y-intercept =

Answer 3

To determine the intercepts of the quadratic function described, we can analyze the information given:

1. X-Intercept: The x-intercept occurs where the graph crosses the x-axis, which is at the point \( (x, 0) \). From your description, the curve crosses the x-axis at \((-1, 0)\). Therefore:

   X-Intercept: \(( -1, 0 )\)

2. Y-Intercept: The y-intercept occurs where the graph crosses the y-axis, which is at the point \( (0, y) \). From your description, the curve crosses the y-axis at \( (0, 2) \). Therefore:

   Y-Intercept: \(( 0, 2 )\)

Summary of Intercepts:

• X-Intercept: \((-1, 0)\)
• Y-Intercept: \((0, 2)\)

Answer 4

Which statement is true about the given function?

f(x) < 0 over the intervals (–infinity, –2.7) and (0.8, infinity).
f(x) < 0 over the intervals (–infinity, –2.7) and
(–1, 0.8).
f(x) > 0 over the intervals (–infinity, –2.7) and
(–1, 0.8).
f(x) > 0 over the intervals (–infinity, –1) and
(0.8, infinity).

Answer 5

To determine which statement is true about the given function, it is important to understand the relationship between the given intervals and the conditions provided.

1. First Statement: \( f(x) < 0 \) over the intervals \((-\infty, -2.7)\) and \((0.8, \infty)\).

   • This means the function is negative in the intervals before \(-2.7\) and after \(0.8\).

2. Second Statement: \( f(x) < 0 \) over the intervals \((-\infty, -2.7)\) and \((-1, 0.8)\).

   • This means the function is negative in the intervals before \(-2.7\) and between \(-1\) and \(0.8\).

3. Third Statement: \( f(x) > 0 \) over the intervals \((-\infty, -2.7)\) and \((-1, 0.8)\).

   • This indicates that the function is positive in the intervals before \(-2.7\) and between \(-1\) and \(0.8\).

4. Fourth Statement: \( f(x) > 0 \) over the intervals \((-\infty, -1)\) and \((0.8, \infty)\).

   • Here, the function is positive in the intervals before \(-1\) and after \(0.8\).

Analyzing the Statements

• For a function to be \( f(x) < 0 \) in certain intervals, it means the graph of the function must cross the x-axis (have roots) at points in those intervals.
• Conversely, \( f(x) > 0 \) indicates the function is above the x-axis in the specified intervals.

Conclusion

To verify which statement might be true, typically more information about the function (such as its roots, general shape, or behavior) would help.

However, from the context of these statements:

• It seems more typical for a polynomial (or related function) to alternate signs as it crosses the x-axis. If \( f(x) < 0 \) in certain intervals, it is likely \( f(x) > 0 \) in others.

Given the intervals provided, the most logical deduction without further insights would be:

The first statement \( f(x) < 0 \) over intervals \((-\infty, -2.7)\) and \((0.8, \infty)\) or the fourth statement \( f(x) > 0 \) over intervals \((-\infty, -1)\) and \((0.8, \infty)\) could both be valid, but without knowing the function's specific details, it’s difficult to ascertain definitively.

If you have more context or graphical details about the function, that would enable a more accurate determination! In the absence of that, we'd recommend the first statement might be typically more correct, as functions are likely to be negative outside of certain roots.

Answer 6

OH im sorry i forgot to give you the graph but thats all right here f(x) < 0 over the intervals (–infinity, –2.7) and
(–1, 0.8).

Use the graph to determine which statement is true about the end behavior of f(x).

As the x-values go to negative infinity, the function’s values go to negative infinity.
As the x-values go to negative infinity, the function’s values go to positive infinity.
As the x-values go to positive infinity, the function’s values go to negative infinity.
As the x-values go to positive infinity, the function’s values go to zero.
The image shows a graph of a cubic function on a coordinate plane. The x-axis ranges from -3 to 3, and the y-axis ranges from -16 to 8. The orange curve has two turning points and passes through four highlighted points, which are likely local maximums, local minimums, or intercepts. This graph provides visual information about the behavior of the cubic function and its critical points, useful for analysis in calculus or algebra.

Answer 7

To determine the end behavior of the function \( f(x) \) based on the graph you've described, we can analyze the characteristics of cubic functions and the information you've provided.

General Properties of Cubic Functions:

1. Cubic functions generally have the form \( f(x) = ax^3 + bx^2 + cx + d \).
2. The end behavior of a cubic function is primarily influenced by the leading coefficient \( a \):
   • If \( a > 0 \), the function rises to positive infinity as \( x \) approaches positive infinity and falls to negative infinity as \( x \) approaches negative infinity.
   • If \( a < 0 \), the function falls to negative infinity as \( x \) approaches positive infinity and rises to positive infinity as \( x \) approaches negative infinity.

Analyzing the Given Statements:

1. As the x-values go to negative infinity, the function’s values go to negative infinity.

2. As the x-values go to negative infinity, the function’s values go to positive infinity.

3. As the x-values go to positive infinity, the function’s values go to negative infinity.

4. As the x-values go to positive infinity, the function’s values go to zero.

Using the Graph Information:

• You mentioned that the cubic function has two turning points and three significant highlighted points (which could include local maximums, minimums, and x-intercepts).
• If the graph rises on the left side (as \( x \) approaches negative infinity) and falls on the right side (as \( x \) approaches positive infinity), this suggests that the leading coefficient \( a \) is positive.

Interpretation:

With the description you provided about the cubic graph:

• If it goes down as \( x \to +\infty \) and goes up as \( x \to -\infty \), that indicates that as \( x \) approaches negative infinity, \( f(x) \) approaches positive infinity.

Thus:

The true statement about the end behavior of \( f(x) \) would be:

• As the x-values go to negative infinity, the function’s values go to positive infinity.

If you can confirm that the left side of the graph rises and the right side falls, this supports the conclusion!

Answer 8

On a coordinate plane, a curved line with a maximum value of (negative 1, 4) and minimum values of (negative 1.25, negative 16) and (2.5, negative 3), crosses the x-axis at (negative 2.1, 0), (0.25, 0), (1.75, 0), and (3, 0), and crosses the y-axis at (0, negative 3).
Which intervals show f(x) decreasing? Check all that apply.

[–2.5, –2]
[–2, –1.5]
[–1, 1)
[1.5, 2]
[2, 2.5)
(2.5, 3]

Answer 9

To determine the intervals where \( f(x) \) is decreasing based on the given information about the graph, we need to examine the behavior of the function over the specified intervals with respect to the maximum and minimum points, as well as the x-intercepts.

Key Features from the Description:

• Maximum Value: \( (-1, 4) \)
• Minimum Values: \( (-1.25, -16) \) and \( (2.5, -3) \)
• X-intercepts: \( (-2.1, 0) \), \( (0.25, 0) \), \( (1.75, 0) \), and \( (3, 0) \)
• Y-intercept: \( (0, -3) \)

Analyzing the Intervals:

1. Interval: \([-2.5, -2]\):

   • As \( x \) moves from \(-2.5\) to \(-2\), the function is increasing towards the maximum at \((-1, 4)\). Not decreasing.

2. Interval: \([-2, -1.5]\):

   • The function is also still increasing in this interval until it reaches the maximum at \((-1, 4)\). Not decreasing.

3. Interval: \([-1, 1)\):

   • In this interval, the function must decrease after reaching the maximum at \((-1, 4)\). Therefore, it is decreasing from this maximum to the first zero at \( (0.25, 0) \). Decreasing.

4. Interval: \([1.5, 2]\):

   • In this interval, the function is decreasing as it approaches the minimum at \( (2.5, -3) \) after crossing the x-axis at \( (1.75, 0) \). Decreasing.

5. Interval: \([2, 2.5)\):

   • During this interval, the function continues to decrease from the x-intercept at \( (2, 0) \) towards the minimum at \( (2.5, -3) \). Decreasing.

6. Interval: \((2.5, 3]\):

   • After the minimum at \( (2.5, -3) \), the function begins to increase towards the x-intercept at \( (3, 0) \). Not decreasing.

Summary of Decreasing Intervals:

The intervals where \( f(x) \) is decreasing are:

• \([-1, 1)\)
• \([1.5, 2]\)
• \([2, 2.5)\)

Final Answer:

The correct intervals showing \( f(x) \) decreasing are:

• *\[ -1, 1) *
• [ 1.5, 2 \]
• *[ 2, 2.5) *

Answer 10

either one of them is wrong or only two is correct

Answer 11

Let’s go through the problem again carefully with a step-by-step approach to identify where \( f(x) \) is decreasing based on the provided information about the function. We'll focus on the critical points and behavior in relation to the x-axis crossings and maximum/minimum points specified.

Given points:

• Maximum: \( (-1, 4) \)
• Minimums: \( (-1.25, -16) \) and \( (2.5, -3) \)
• X-intercepts: \( (-2.1, 0) \), \( (0.25, 0) \), \( (1.75, 0) \), and \( (3, 0) \)
• Y-intercept: \( (0, -3) \)

Analyzing Each Interval

1. Interval: \([-2.5, -2]\):

   • From slightly before \(-2.1\) to \(-2\), the function is increasing from a value lower than 0 towards it as it approaches the x-axis. Not decreasing.

2. Interval: \([-2, -1.5]\):

   • The function continues to rise as it approaches the maximum at \((-1, 4)\) from the left. Not decreasing.

3. Interval: \([-1, 1)\):

   • This interval starts at the maximum at \((-1, 4)\) and decreases to the x-intercept at \( (0.25, 0) \) before rising again. Decreasing.

4. Interval: \([1.5, 2]\):

   • The function drops down from the x-intercept at \( (1.75, 0) \) leading downwards towards the minimum at \( (2.5, -3) \). Decreasing.

5. Interval: \([2, 2.5)\):

   • Still decreasing as it goes from the second x-intercept at \( (2, 0) \) down to the minimum at \( (2.5, -3) \). Decreasing.

6. Interval: \((2.5, 3]\):

   • After the minimum at \( (2.5, -3) \), the graph starts increasing again towards the x-intercept at \( (3, 0) \). Not decreasing.

Conclusion

Based on the above analysis, the intervals where \( f(x) \) is decreasing are:

• \([-1, 1)\)
• \([1.5, 2]\)
• \([2, 2.5)\)

If you need to check again for potential misunderstanding:

• Correct Decreasing Intervals: \([-1, 1)\), \([1.5, 2]\), and \([2, 2.5)\).

From your follow-up, it seems there could be a misinterpretation of the context. The key take-home is that the intervals \([-1, 1)\) and \([1.5, 2]\) are definitely decreasing, and \([2, 2.5)\) is also decreasing until it reaches the min point.

If there are discrepancies, confirming the exact shape of the graph would be necessary, but, as highlighted, these three intervals are the ones where the function is decreasing.