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Graphing Polynomial Functions quiz

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  • What information do you need to start graphing a polynomial function?
    You need to identify known points such as x-intercepts, y-intercepts, and turning points, as well as determine the end behavior.
  • How do you determine the end behavior of a polynomial function?
    The end behavior is determined by the leading coefficient and the degree of the polynomial.
  • What is the process for finding x-intercepts of a polynomial function?
    Set the polynomial equal to zero and solve for x to find the x-intercepts.
  • How do you find the y-intercept of a polynomial function?
    Evaluate the polynomial at x = 0 to find the y-intercept.
  • What does the multiplicity of an x-intercept tell you about the graph at that point?
    Multiplicity tells you whether the graph crosses the x-axis (odd multiplicity) or touches and turns around (even multiplicity).
  • How can you fill in unknown intervals on the graph of a polynomial function?
    Select x-values within the unknown intervals, calculate their f(x) values, and plot these points to clarify the graph's shape.
  • What is the maximum number of turning points a polynomial function can have?
    The maximum number of turning points is the degree of the polynomial minus one.
  • Why is it important to plot points in unknown intervals when graphing a polynomial?
    Plotting points in unknown intervals helps reveal the graph's behavior between known points, making the graph more accurate.
  • What should you do after plotting all known and calculated points on a polynomial graph?
    Connect all points with a smooth, continuous curve to complete the graph.
  • How do you check if your polynomial graph is correct regarding turning points?
    Verify that the number of turning points does not exceed the degree minus one.
  • What is the significance of the leading coefficient being positive in a cubic polynomial?
    A positive leading coefficient means the graph rises on the right side as x approaches infinity.
  • How does the degree of a polynomial affect its end behavior?
    An odd degree means the ends of the graph go in opposite directions; an even degree means both ends go the same way.
  • What is a good strategy for choosing x-values in unknown intervals?
    Choose x-values that are easy to plot and provide useful information about the graph's shape.
  • What happens at an x-intercept with odd multiplicity?
    The graph crosses the x-axis at that point.
  • What is the final step in graphing a polynomial function?
    The final step is to check the number of turning points and ensure the graph matches the expected end behavior.