Local Minimum Intervals Quiz & Flashcards on Graphs

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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]?

What are the intercepts of the graphed function?

x-intercept = (-1, 0), y-intercept = (0, -3) Signup and view all the answers

When f(x) = 0, x =?

-1.8 Signup and view all the answers

What is the local maximum over the interval [-3, 1.5] for the graphed function?

56 Signup and view all the answers

As the x-values go to positive infinity, the function's values go to negative infinity?

True Signup and view all the answers

Which statements about the local maximums and minimums for the given function are true? (Check all that apply)

Over the interval [1, 4], the local maximum is 0. Signup and view all the answers

Which interval for the graphed function has a local minimum of 0?

[2, 4] Signup and view all the answers

Which statement correctly identifies a local minimum of the graphed function?

Over the interval [-1, 0.5], the local minimum is 1. Signup and view all the answers

As the x-values go to positive infinity, the function's values go to positive infinity?

True Signup and view all the answers

Which interval for the graphed function contains the local maximum?

[0, 2] Signup and view all the answers

Which statement is true about the local minimum of the graphed function?

Over the interval [4, 7], the local minimum is -7. Signup and view all the answers

F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)?

True Signup and view all the answers

Which is an x-intercept of the graphed function?

True Signup and view all the answers

Which is a y-intercept of the graphed function?

True Signup and view all the answers

Which lists all of the x-intercepts of the graphed function?

(1, 0), (2, 0), and (-3, 0) Signup and view all the answers

Which lists all of the y-intercepts of the graphed function?

(0, -3) Signup and view all the answers

Which interval for the graphed function contains the local maximum?

[1, 2] Signup and view all the answers

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.