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Graphing Polynomial Functions quiz

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  • What is the first step in graphing a polynomial function?
    The first step is to determine the end behavior by analyzing the leading coefficient and degree of the polynomial.
  • How do you find the x-intercepts of a polynomial function?
    Set f(x) = 0 and solve for x, often by factoring the polynomial.
  • What does the multiplicity of an x-intercept tell you about the graph?
    Multiplicity indicates whether the graph crosses or touches the x-axis at that intercept; odd multiplicity means it crosses, even means it touches.
  • How do you find the y-intercept of a polynomial function?
    Evaluate f(0) by plugging x = 0 into the polynomial.
  • What is the end behavior of the function 2x^3 - 6x^2 + 6x - 2?
    Since the leading coefficient is positive and the degree is odd, the graph rises to the right and falls to the left.
  • How do you determine intervals of unknown behavior when graphing a polynomial?
    Divide the graph between known points such as intercepts and end behavior, creating intervals where the graph's behavior is uncertain.
  • Why is it important to plot points in intervals of unknown behavior?
    Plotting points in these intervals helps clarify the graph's shape between known points and ensures accuracy.
  • What strategic x-values should you choose to plot in unknown intervals?
    Choose x-values that are easy to plot and close to known points, avoiding extreme values that are hard to graph.
  • For the function 2x^3 - 6x^2 + 6x - 2, what are the x-intercepts and their behavior?
    The x-intercept is at x = 1 with multiplicity 3, so the graph crosses the x-axis at this point.
  • What is the y-intercept for 2x^3 - 6x^2 + 6x - 2?
    The y-intercept is at (0, -2).
  • How many turning points can a degree 3 polynomial have?
    A degree 3 polynomial can have at most 2 turning points, which is degree minus 1.
  • What is the purpose of connecting plotted points with a smooth curve?
    Connecting points with a smooth curve ensures the graph reflects the continuous nature and end behavior of the polynomial.
  • What should you check after graphing a polynomial function?
    Check that the number of turning points does not exceed the maximum allowed by the degree and that the end behavior matches expectations.
  • What is a good x-value to plot in the interval from negative infinity to 0 for the function 2x^3 - 6x^2 + 6x - 2?
    x = -1 is a strategic choice, and f(-1) = -16.
  • What is the result of plugging x = 3 into 2x^3 - 6x^2 + 6x - 2?
    Plugging in x = 3 gives f(3) = 16, which is a point to plot in the interval from 1 to infinity.