5 Questions
Which equations are shown in the first graph in the textbook?
$y=x^{1/3}$, $y=x^{2/3}$, $y=x^{4/3}$
What is the equation shown in the second graph in the textbook?
$y=x^{1/4}$
At which $x$ value do the graphs of all the equations show an asymptote?
$x=0$
Which type of asymptotes do all the equations have?
Both vertical and horizontal asymptotes
What is the common topic discussed in the textbook excerpt?
Asymptotes
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.
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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