1. On a coordinate plane, a curved line with a minimum value of (negative 2.5, negative 12) and a maximum value of (0, negative 3) crosses the x-axis at (negative 4, 0) and crosses the y-axis at (0, negative 3).
Which statement is true about the graphed function?
F(x) < 0 over the interval (–∞, –4)
F(x) < 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –4)
2. On a coordinate plane, a curved line with minimum values of (negative 1.56, negative 6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (negative 2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0).
Which interval for the graphed function has a local minimum of 0?
[–3, –2]
[–2, 0]
[1, 2]
[2, 4]
3. Which function is positive for the entire interval [–3, –2]?
On a coordinate plane, a curved line with a minimum value of (0, negative 3) crosses the x-axis at (negative 3, 0) and (3, 0), and crosses the y-axis at (0, negative 3).
On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).
On a coordinate plane, a curved line with a minimum value of (2, 4) and a maximum value of (0.5, 6), crosses the x-axis at (negative 1.5, 0) and crosses the y-axis at (0, 5).
On a coordinate plane, a curved line with a minimum value of (negative 1.75, negative 3.9) and a maximum value of (0, 2), crosses the x-axis at (negative 2.2, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2).
4. On a coordinate plane, a curved line with minimum values of (negative 1.5, negative 2) and (1.5, 2), and a maximum value of (0, 4), crosses the x-axis at (negative 2, 0), (negative 1, 0), (1, 0), and (2, 0), and crosses the y-axis at (0, 4).
Which is an x-intercept of the graphed function?
(0, 4)
(–1, 0)
(4, 0)
(0, –1)
5. On a coordinate plane, a curved line crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 0.25). The line exits the plane at (negative 2, negative 6) and (2, 6).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero
As the x-values go to positive infinity, the function's values go to positive infinity.
6. On a coordinate plane, a curved line with a minimum value of (negative 1.25, negative 3.25) and a maximum value of (0.25, negative 1.75), crosses the x-axis at (negative 2.25, 0), and crosses the y-axis at (0, negative 2). The line exits the plane at (negative 2.75, 6) and (1.5, 6).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to positive infinity, the function's values go to positive infinity.
7. On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).
8. On a coordinate plane, a curved line with a minimum value of (0, negative 9) and maximum values of (negative 2.3, 16) and (2.3, 16), crosses the x-axis at (negative 3, 0), (negative 1, 0), (1, 0), and (3, 0), and crosses the y-axis at (0, negative 9).
Which is a y-intercept of the graphed function?
(–9, 0)
(–3, 0)
(0, –9)
(0, –3)
9. On a coordinate plane, a curved line with a minimum value of (5.1, negative 7) and a maximum value of (0, 25), crosses the x-axis at (negative 3.4, 0), (3.9, 0), and (6, 0), and crosses the y-axis at (0, 25).
Which statement is true about the local minimum of the graphed function?
Over the interval [–4, –2], the local minimum is 0.
Over the interval [–2, –1], the local minimum is 25.
Over the interval [–1, 4], the local minimum is 0.
Over the interval [4, 7], the local minimum is -7.
10. On a coordinate plane, a curved line crosses the x-axis at (negative 1, 0), and crosses the y-axis at (0, negative 3).
What are the intercepts of the graphed function?
Statement about F(x): The function has a maximum at (0, -3) and crosses the x-axis at (-4, 0).
Correct Answer: F(x) < 0 over the interval (–∞, –4). The function is negative for all x-values less than -4.
Interval for local minimum of 0: The function crosses the x-axis at (0, 0) which suggests it is equal to 0 at that point.
Correct Answer: [–2, 0]. The function is 0 at two x-intercepts including 0.
Function positive for entire interval [–3, –2]: Among the given functions, we need to see which function does not cross the x-axis in this interval [–3, –2].
Correct Answer: On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).
X-intercept of the graphed function: The x-intercepts are where the function crosses the x-axis.
Correct Answer: (–1, 0).
Statement about end behavior: The function crosses the x-axis at (-1, 0) and goes towards negative infinity at (-2, -6).
Correct Answer: As the x-values go to negative infinity, the function's values go to negative infinity.
Statement about end behavior: The function's y-value decreases as x approaches negative infinity and may increase or hit a maximum going towards positive infinity.
Correct Answer: As the x-values go to positive infinity, the function's values go to positive infinity.
True statement about the graphed function: We look for intervals that are part of or fully below or above the x-axis.
Correct Answer: F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
Y-intercept of the graphed function: The y-intercept occurs where the graph intersects the y-axis.
Correct Answer: (0, –9).
Statement about local minimum of the graphed function: Looking at intervals concerning where the minimums occur.
Correct Answer: Over the interval [4, 7], the local minimum is -7.
If you have any more questions or if you need further clarification on any of these solutions, feel free to ask!
for 3 which graph 1 2 3 or 4? and for 5 when you said As the x-values go to negative infinity, the function's values go to negative infinity**.
the only one that says negative is this As the x-values go to negative infinity, the function's values are equal to zero
so either thats what you meant or its wrong
Let's clarify your questions about problems 3 and 5.
Problem 3
You need to identify which of the four graphs has the correct characteristics to be positive over the interval [-3, -2].
Graph 1: Has a minimum value at (0, -3) and crosses the x-axis at (-3, 0) and (3, 0). This graph would be negative from -3 down to -2.
Graph 2: Has a minimum at (2, -3) and crosses the x-axis at (-1, 0) and (5, 0). This graph would be negative for all values between -1 and any point before 0, thus negative in the interval [-3, -2].
Graph 3: Has a minimum value at (2, 4) which suggests that it is positive over the interval [-3, -2].
Graph 4: Has a local minimum below zero, meaning that it doesn’t meet the criteria.
Correct Answer: Graph 3 would be the correct interpretation as it maintains positive values over the entire interval [-3, -2].
Problem 5
Let's clarify the statements regarding end behavior:
The graph crosses the x-axis at (-1, 0), which means it is zero at that point. If it is decreasing to exit the plane at (-2, -6), that suggests that as you go towards negative infinity on the x-axis, the function goes to negative values, not zero. The statement I mentioned about going to negative infinity as x approaches negative infinity was based on the interpretation of being negative.
The other option you noted: "As the x-values go to negative infinity, the function's values are equal to zero" cannot be true as you point out it is not consistent with the graph behavior given it exits below zero.
Given this, the correct answer would actually be that the function's values go to negative infinity as x approaches negative infinity.
Correct Answer: As the x-values go to negative infinity, the function's values go to negative infinity.
Thank you for highlighting that, and I'm glad to clarify these points! If you have any more questions or concerns, feel free to ask!
the thing is for number 5 that option isnt included As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero
As the x-values go to positive infinity, the function's values go to positive infinity.
it has to be one of them
Thank you for your patience and clarification regarding Question 5. Let's analyze the possibilities based on the available options:
Given the graph described:
It crosses the x-axis at (-1, 0) and has y-values ranging downward at (-2, -6) and upward at (2, 6).
Options Available:
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to positive infinity, the function's values go to positive infinity.
Analysis of Each Option:
As x goes to positive infinity: The graph eventually rises towards positive infinity as it increases in positive x-values, so this is incorrect.
As x goes to zero: The function does not approach positive infinity; it is at (0, 0.25) so it’s above zero, not tending to infinity.
As the x-values go to negative infinity: The graph indeed exits downward at (-2, -6), suggesting values fall below zero, so this is incorrect as well.
As x goes to positive infinity: The function rises towards positive values; thus, this statement holds true.
Conclusion:
Considering your clarification:
Correct Answer: As the x-values go to positive infinity, the function's values go to positive infinity.
I apologize for the earlier confusion and appreciate your understanding as we sorted through this issue! If you have further questions, please feel free to ask.
50!?!?!? please re do some of the questions please
Sure! Let's redo the relevant questions carefully one by one. Please specify which questions you'd like me to revisit, or I can go through them step by step from the beginning. Just let me know!
1. On a coordinate plane, a curved line with a minimum value of (0.8, negative 11.4) and maximum values of (negative 1.6, 56) and (2, 0), crosses the x-axis at (negative 2.5, 0), (0, 0), and (2, 0), and crosses the y-axis at (0, 0).
What is the local maximum over the interval [–3, 1.5] for the graphed function?
0
56
–11.4
2
2. On a coordinate plane, a curved line with minimum values of (negative 2, 0) and (1.05, negative 41), and a maximum value of (negative 0.5, 5), crosses the x-axis at (negative 2, 0), (0, 0), and (1.5, 0), and crosses the y-axis at (0, 0).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function’s values go to positive infinity.
As the x-values go to zero, the function’s values go to positive infinity.
As the x-values go to negative infinity, the function’s values are equal to zero.
As the x-values go to negative infinity, the function’s values go to negative infinity.
3. On a coordinate plane, a curved line with minimum values of (negative 1.56, negative 6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (negative 2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0).
Which interval for the graphed function has a local minimum of 0?
[–3, –2]
[–2, 0]
[1, 2]
[2, 4]
4. On a coordinate plane, a curved line with a minimum value of (negative 1.25, negative 3.25) and a maximum value of (0.25, negative 1.75), crosses the x-axis at (negative 2.25, 0), and crosses the y-axis at (0, negative 2). The line exits the plane at (negative 2.75, 6) and (1.5, 6).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to positive infinity, the function's values go to positive infinity.
5. On a coordinate plane, a curved line with a minimum value of (negative 2.5, negative 12) and a maximum value of (0, negative 3) crosses the x-axis at (negative 4, 0) and crosses the y-axis at (0, negative 3).
Which statement is true about the graphed function?
F(x) < 0 over the interval (–∞, –4)
F(x) < 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –4)
6. On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).
7. On a coordinate plane, a curved line with a minimum value of (5.1, negative 7) and a maximum value of (0, 25), crosses the x-axis at (negative 3.4, 0), (3.9, 0), and (6, 0), and crosses the y-axis at (0, 25).
Which statement is true about the local minimum of the graphed function?
Over the interval [–4, –2], the local minimum is 0.
Over the interval [–2, –1], the local minimum is 25.
Over the interval [–1, 4], the local minimum is 0.
Over the interval [4, 7], the local minimum is -7.
8. On a coordinate plane, a curved line with a minimum value of (1.5, negative 1) and a maximum value of (negative 1.5, 13), crosses the x-axis at (negative 3, 0), (1, 0), and (2, 0), and crosses the y-axis at (0, 6).
Which lists all of the x-intercepts of the graphed function?
(0, 6)
(1, 0) and (2, 0)
(1, 0), (2, 0), and (–3, 0)
(1, 0), (2, 0), (–3, 0), and (0, 6)
9. On a coordinate plane, a curved line with a minimum value of (0, negative 9) and maximum values of (negative 2.3, 16) and (2.3, 16), crosses the x-axis at (negative 3, 0), (negative 1, 0), (1, 0), and (3, 0), and crosses the y-axis at (0, negative 9).
Which is a y-intercept of the graphed function?
(–9, 0)
(–3, 0)
(0, –9)
(0, –3)
10. On a coordinate plane, a curved line crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 0.25). The line exits the plane at (negative 2, negative 6) and (2, 6).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero
As the x-values go to positive infinity, the function's values go to positive infinity.
Let's carefully reassess each of the questions you mentioned. I’ll provide clear explanations for my answers.
Question 1:
The function has local extrema and crosses the x-axis at several points. The maximum value over the interval \([-3, 1.5]\) is identified at the highest point:
Local maximum is at \((–1.6, 56)\), which is within the given interval.
The function reaches 0 at \(x = 2\) and also crosses the x-axis at those points.
Answer: 56.
Question 2:
For the end behavior of a function, we look at how the function behaves as \(x\) approaches positive or negative infinity. Since the maximum is negative, this suggests that the function goes to negative infinity as \(x\) approaches negative infinity.
Answer: As the x-values go to negative infinity, the function’s values go to negative infinity.
Question 3:
The function crosses the x-axis at \(0\) within the interval \([-2, 0]\). This means the function takes the value of \(0\) at that point.
Answer: [–2, 0] (since the function achieves a local minimum of 0 at that interval).
Question 4:
In this case, we are examining the behavior of the graphed function as it approaches both positive and negative infinity.
The function exits the plane at \( (1.5, 6) \), indicating that it rises, leading to positive values.
Answer: As the x-values go to positive infinity, the function's values go to positive infinity.
Question 5:
The function crosses the x-axis at \((-4, 0)\), indicating that all values to the left of -4 will be negative when \(F(x)\) maintains values below zero at the local maximum values.
Answer: F(x) < 0 over the interval (–∞, –4).
Question 6:
We need to determine which intervals exhibit positive or negative ranges.
The function has x-intercepts, meaning it is below the x-axis between the intervals defined.
Answer: F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
Question 7:
Examining the local minimum at \( (5.1, -7) \), we need to observe how the function behaves in the specified intervals.
The local minimum occurs at the mentioned value \((5.1, -7)\).
Answer: Over the interval [4, 7], the local minimum is -7.
Question 8:
The x-intercepts occur where the graph crosses the x-axis. The values explicitly mentioned are:
\( (–3, 0), (1, 0), (2, 0) \)
Answer: (1, 0), (2, 0), and (–3, 0).
Question 9:
The y-intercept occurs where the graph crosses the y-axis at \( (0, -9) \).
Answer: (0, –9).
Question 10:
This question evaluates the end behavior of the function. As it exits the plane at two points (\( (−2,−6) \) and \( (2, 6) \)), we can observe:
The function should go to positive infinity as \(x\) approaches positive infinity.
Answer: As the x-values go to positive infinity, the function's values go to positive infinity.
Please let me know if you have specific questions or need further clarification on any of these solutions!
50??! AGAIN
i need 70
1. On a coordinate plane, a curved line with minimum values of (negative 0.8, negative 2.8) and (3, 0), and a maximum value of (1.55, 10.8), crosses the x-axis at (negative 2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0).
Which interval for the graphed function contains the local maximum?
[–3, –2]
[–2, 0]
[0, 2]
[2, 4]
2. On a coordinate plane, a curved line crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 0.25). The line exits the plane at (negative 2, negative 6) and (2, 6).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero
As the x-values go to positive infinity, the function's values go to positive infinity.
3. On a coordinate plane, a curved line with a minimum value of (negative 1.25, negative 3.25) and a maximum value of (0.25, negative 1.75), crosses the x-axis at (negative 2.25, 0), and crosses the y-axis at (0, negative 2). The line exits the plane at (negative 2.75, 6) and (1.5, 6).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to positive infinity, the function's values go to positive infinity.
4. On a coordinate plane, a curved line with a minimum value of (0, negative 9) and maximum values of (negative 2.3, 16) and (2.3, 16), crosses the x-axis at (negative 3, 0), (negative 1, 0), (1, 0), and (3, 0), and crosses the y-axis at (0, negative 9).
Which is a y-intercept of the graphed function?
(–9, 0)
(–3, 0)
(0, –9)
(0, –3)
5. On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).
6. On a coordinate plane, a curved line with minimum values of (negative 0.5, negative 7) and (2.5, negative 1), and a maximum value of (1.5, 1), crosses the x-axis at (negative 1, 0), (1, 0), and (3, 0), and crosses the y-axis at (0, negative 6).
Which interval for the graphed function contains the local maximum?
[–1, 0]
[1, 2]
[2, 3]
[3, 4]
7. On a coordinate plane, a curved line with a minimum value of (1.5, negative 1) and a maximum value of (negative 1.5, 13), crosses the x-axis at (negative 3, 0), (1, 0), and (2, 0), and crosses the y-axis at (0, 6).
Which lists all of the x-intercepts of the graphed function?
(0, 6)
(1, 0) and (2, 0)
(1, 0), (2, 0), and (–3, 0)
(1, 0), (2, 0), (–3, 0), and (0, 6)
8. On a coordinate plane, a curved line with minimum values of (negative 1.56, negative 6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (negative 2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0).
Which interval for the graphed function has a local minimum of 0?
[–3, –2]
[–2, 0]
[1, 2]
[2, 4]
9. Which function is positive for the entire interval [–3, –2]?
On a coordinate plane, a curved line with a minimum value of (0, negative 3) crosses the x-axis at (negative 3, 0) and (3, 0), and crosses the y-axis at (0, negative 3).
On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).
On a coordinate plane, a curved line with a minimum value of (2, 4) and a maximum value of (0.5, 6), crosses the x-axis at (negative 1.5, 0) and crosses the y-axis at (0, 5).
On a coordinate plane, a curved line with a minimum value of (negative 1.75, negative 3.9) and a maximum value of (0, 2), crosses the x-axis at (negative 2.2, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2).
10. On a coordinate plane, a curved line crosses the x-axis at (negative 1, 0), and crosses the y-axis at (0, negative 3).
What are the intercepts of the graphed function?
Let’s go through each question step by step to ensure clarity and correctness.
Question 1:
Description: The function has a minimum at (-0.8, -2.8) and a maximum at (1.55, 10.8). It crosses the x-axis at (-2.5, 0), (0, 0), and (3, 0).
Local Maximum Interval: The local maximum occurs at (1.55, 10.8), which is within the interval [–2, 0].
Answer:[–2, 0]
Question 2:
Description: The function crosses the x-axis at (-1, 0) and the y-axis at (0, 0.25). It exits the plane at (-2, -6) and (2, 6).
End Behavior: As \(x\) approaches positive infinity, the function exits to positive infinity (as it goes up towards (2, 6)), and as \(x\) goes to negative infinity, it heads downwards (to (-2, -6)).
Answer:As the x-values go to positive infinity, the function's values go to positive infinity.
Question 3:
Description: The function has a minimum at (-1.25, -3.25) and a maximum at (0.25, -1.75). It crosses the x-axis at (-2.25, 0) and y-axis at (0, -2).
End Behavior: As \(x\) approaches positive infinity, this function should eventually go to negative infinity as it exhibits a maximum below zero at (-1.75).
Answer:As the x-values go to positive infinity, the function's values go to negative infinity.
Question 4:
Description: The function crosses the x-axis at multiple points. Its y-axis crossing is visible at (0, -9).
Y-Intercept: The point at which the graph crosses the y-axis directly is (0, -9).
Answer:(0, –9)
Question 5:
Description: The function crosses the x-axis at multiple points, so we need to analyze intervals where the function is negative or positive.
It is above zero in the intervals indicated.
F(x) < 0 occurs when the function is below the x-axis.
Answer:F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
Question 6:
Description: The function has a local maximum at (1.5, 1) and crosses the x-axis at points visible around the defined intervals.
Local Maximum Interval: This occurs in the interval [1, 2].
Answer:[1, 2]
Question 7:
Description: The function has x-intercepts at (-3, 0), (1, 0), and (2, 0).
X-Intercepts: The question asks for all x-intercepts of which the options contain correct intersections.
Answer:(1, 0), (2, 0), and (–3, 0).
Question 8:
Description: The function has a local minimum at (1.56, -6) and also shows multiple x-intercepts.
Local Minimum of 0: The function crosses the x-axis at (0, 0), indicating a local minimum contained within that range.
Answer:[–2, 0]
Question 9:
Description: We need to identify which graph function remains positive throughout the specified interval.
The graph must not cross the x-axis between -3 and -2.
Answer:The function with a minimum value of (2, 4) is the one that is positive throughout [–3, –2].
Question 10:
Description: The graph crosses the x-axis at (-1, 0) and the y-axis at (0, -3).
