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?Sketch the graph of an example of a function f that satisfies all of the given
Chapter 2, Problem 7(choose chapter or problem)
Sketch the graph of an example of a function f that satisfies all of the given conditions
\(\lim _{x \rightarrow 0} f(x)=\infty\), \(\lim _{x \rightarrow 3^{-}} f(x)=-\infty\), \(\lim _{x \rightarrow 3^{+}} f(x)=\infty\), \(\lim _{x \rightarrow-\infty} f(x)=1\), \(\lim _{x \rightarrow \infty} f(x)=-1\)
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QUESTION:
Sketch the graph of an example of a function f that satisfies all of the given conditions
\(\lim _{x \rightarrow 0} f(x)=\infty\), \(\lim _{x \rightarrow 3^{-}} f(x)=-\infty\), \(\lim _{x \rightarrow 3^{+}} f(x)=\infty\), \(\lim _{x \rightarrow-\infty} f(x)=1\), \(\lim _{x \rightarrow \infty} f(x)=-1\)
ANSWER:Step 1 of 3
\(\lim _{x \rightarrow 0} f(x)=\infty \Longrightarrow\) vertical asymptote going upwards at x = 0
\(\lim _{x \rightarrow 3^{-}} f(x)=-\infty \Longrightarrow\) vertical asymptote going downwards from left, x = 3
\(\lim _{x \rightarrow 3^{+}} f(x)=\infty \Longrightarrow\) vertical asymptote going upwards from right, x = 3
\(\lim _{x \rightarrow-\infty} f(x)=1 \Longrightarrow\) horizontal asymptote going left, y = 1
\(\lim _{x \rightarrow \infty} f(x)=-1 \Longrightarrow\) horizontal asymptote going right, y = -1
The graph below satisfies all the conditions described above:
Note that there are infinitely many possible answers, this is just one example.
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