Questions and Answers
F(x) > 0 over the interval (-∞, -4)?
True
What are the x-intercepts of the graphed function?
(-3, 0) and (1, 0)
Which function is positive for the entire interval [-3, -2]?
b
What are the intercepts of the graphed function?
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When f(x) = 0, x =?
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What is the local maximum over the interval [-3, 1.5] for the graphed function?
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As the x-values go to positive infinity, the function's values go to negative infinity?
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Which statements about the local maximums and minimums for the given function are true? (Check all that apply)
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Which interval for the graphed function has a local minimum of 0?
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Which statement correctly identifies a local minimum of the graphed function?
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As the x-values go to positive infinity, the function's values go to positive infinity?
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Which interval for the graphed function contains the local maximum?
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Which statement is true about the local minimum of the graphed function?
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F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)?
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Which is an x-intercept of the graphed function?
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Which is a y-intercept of the graphed function?
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Which lists all of the x-intercepts of the graphed function?
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Which lists all of the y-intercepts of the graphed function?
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Which interval for the graphed function contains the local maximum?
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Study Notes
Graph Analysis Key Points
- The function is positive (F(x) > 0) in the interval (-∞, -4).
- The x-intercepts of the function are located at (-3, 0) and (1, 0).
- Another function, referred to as "b", remains positive throughout the interval [-3, -2].
- The intercepts include x-intercept at (-1, 0) and y-intercept at (0, -3).
- When f(x) = 0, the value of x is -1.8.
- The local maximum within the interval [-3, 1.5] is 56.
- End behavior indicates that as x approaches positive infinity, the function values decline towards negative infinity.
- Several local minima and maxima occur:
- Local minimum of -8 over the intervals [-1, 1], [2, 4], and [3, 5].
- Local maximum of 0 within the interval [1, 4].
- The interval [2, 4] achieves a local minimum of 0.
- In the interval [-1, 0.5], a local minimum value of 1 is observed.
- Another aspect of end behavior shows that as x approaches positive infinity, the function values increase towards positive infinity.
- The interval [0, 2] contains a local maximum.
- A local minimum of -7 exists in the interval [4, 7].
- The function is negative (F(x) < 0) over intervals (-∞, -0.7) and (0.76, 2.5).
- An x-intercept noted is (-1, 0).
- The y-intercept is set at (0, -9).
- The complete list of x-intercepts includes (1, 0), (2, 0), and (-3, 0).
- There is only one y-intercept, recorded as (0, -3).
- The interval [1, 2] also contains a local maximum for the function.
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Test your knowledge on analyzing functions with these flashcards. Each card presents a question regarding properties of graphed functions, such as intercepts and positivity on intervals. Perfect for students looking to reinforce their understanding of graphs in mathematics.