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Questions and Answers
Which equations are shown in the first graph in the textbook?
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?
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?
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?
Which type of asymptotes do all the equations have?
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What is the common topic discussed in the textbook excerpt?
What is the common topic discussed in the textbook excerpt?
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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.
