Polynomial Functions and Transformations
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Questions and Answers

What is a key characteristic of all the polynomial functions listed when graphed?

  • They all have horizontal asymptotes.
  • They all have the same y-intercept.
  • They all pass through the origin. (correct)
  • They all exhibit oscillating behavior.

    • How does the end behavior of even-degree polynomials differ from that of odd-degree polynomials?

  • Even-degree polynomials rise on both ends while odd-degree polynomials have opposite behavior. (correct)
  • Even-degree polynomials lead towards infinity in opposite directions.
  • Odd-degree polynomials exhibit linear growth as they approach the ends.
  • Odd-degree polynomials can only approach zero at both ends.

    • What effect does adding +1 to the function f(x) = x³ have on the graph?

  • It causes a horizontal shift to the left.
  • It results in a vertical shift upwards. (correct)
  • It reflects the graph across the x-axis.
  • It alters the degree of the polynomial.

    • What transformation does the equation g(x) = (x - 2)⁴ represent compared to g(x) = x⁴?

    <p>A horizontal shift to the right.</p> Signup and view all the answers

    What effect does the transformation in h(x) = -(x + 5)⁵ - 2 have on the original function p(x) = x⁵?

    <p>It translates the graph downwards and reflects it across the x-axis.</p> Signup and view all the answers

    Which polynomial function has the steepest increase near the origin based on its degree?

    <p>p(x) = x⁵</p> Signup and view all the answers

    How do the graphs of the even-degree and odd-degree polynomials differ in terms of symmetry?

    <p>Even-degree polynomials exhibit symmetry about the y-axis.</p> Signup and view all the answers

    What is the maximum number of x-intercepts that the function g(x) = (x - 2)⁴ can have?

    <p>1</p> Signup and view all the answers

    When observing the end behavior of l(x) = x⁶, what can be concluded about its behavior as x approaches negative infinity?

    <p>l(x) approaches positive infinity.</p> Signup and view all the answers

    What effect does the graph of h(x) = -(x + 5)⁵ - 2 have compared to the base function p(x) = x⁵?

    <p>It reflects the graph over the x-axis and shifts it left.</p> Signup and view all the answers

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