Asymptotes of Functions Graphs
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Questions and Answers

Which equations are shown in the first graph in the textbook?

  • $y=x^{1/4}$, $y=x^{2/4}$, $y=x^{4/4}$
  • $y=x^{1/2}$, $y=x^{2/2}$, $y=x^{4/2}$
  • $y=x^{1/5}$, $y=x^{2/5}$, $y=x^{4/5}$
  • $y=x^{1/3}$, $y=x^{2/3}$, $y=x^{4/3}$ (correct)
  • What is the equation shown in the second graph in the textbook?

  • $y=x^{3/4}$
  • $y=x^{1/4}$ (correct)
  • $y=x^{2/4}$
  • $y=x^{4/4}$
  • At which $x$ value do the graphs of all the equations show an asymptote?

  • $x=1$
  • $x=0$ (correct)
  • $x=2$
  • $x=-1$
  • Which type of asymptotes do all the equations have?

    <p>Both vertical and horizontal asymptotes</p> Signup and view all the answers

    What is the common topic discussed in the textbook excerpt?

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

    Study Notes

    Asymptotes

    • Asymptotes are a key concept in graph analysis, and determining their location is crucial.

    Graphs with Asymptotes

    • The graphs of functions $y=x^{1/3}$, $y=x^{2/3}$, and $y=x^{4/3}$ all have an asymptote at $x=0$.
    • The graph of the function $y=x^{1/4}$ also has an asymptote at $x=0$.

    Nature of Asymptotes

    • All of these functions have both vertical and horizontal asymptotes.
    • The nature of asymptotes depends on the function and can be determined by analyzing the graph.

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    Description

    Identify the nature of asymptotes in various functions and their graphical representations. Learn how to determine the location of asymptotes with examples from the graphs of equations.

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