Analyzing Graphs Flashcards

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Questions and Answers

F(x) > 0 over the interval (-∞, -4)?

True (A)

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?

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

When f(x) = 0, x =?

<p>-1.8</p> Signup and view all the answers

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

<p>56</p> Signup and view all the answers

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

<p>True (A)</p> Signup and view all the answers

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

<p>Over the interval [1, 4], the local maximum is 0. (A), Over the interval [3, 5], the local minimum is -8. (B), Over the interval [2, 4], the local minimum is -8. (C), Over the interval [-1, 1], the local minimum is -8. (D)</p> Signup and view all the answers

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

<p>[2, 4]</p> Signup and view all the answers

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

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

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

<p>True (A)</p> Signup and view all the answers

Which interval for the graphed function contains the local maximum?

<p>[0, 2]</p> Signup and view all the answers

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

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

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

<p>True (A)</p> Signup and view all the answers

Which is an x-intercept of the graphed function?

<p>True (A)</p> Signup and view all the answers

Which is a y-intercept of the graphed function?

<p>True (A)</p> Signup and view all the answers

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

<p>(1, 0), (2, 0), and (-3, 0)</p> Signup and view all the answers

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

<p>(0, -3)</p> Signup and view all the answers

Which interval for the graphed function contains the local maximum?

<p>[1, 2]</p> Signup and view all the answers

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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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