Saylilbaby
  • Saylilbaby
1. Give the domain, range, intercepts, asymptotes, intervals of increasing and decreasing, intervals of positive and negative, symmetry and extrema (if any) for the graph of this equation. Include a screen shot of the graph.
Mathematics
chestercat
  • chestercat
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Saylilbaby
  • Saylilbaby
\[f(x)=\frac{ 3 }{ x^2-4 }+1\]
amoodarya
  • amoodarya
what part of question ,is your problem ?
Saylilbaby
  • Saylilbaby
2. Explain why there are asymptotes for this graph and how to find them algebraically. Use vocabulary given in the text for this module. 3. Algebraically calculate the intercepts, both x and y. Show all work and state extraneous solutions, if any.

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amoodarya
  • amoodarya
\[vertical-retrice\rightarrow x^-4=0 \rightarrow x=\pm 2\\ \lim_{x \rightarrow 2}f(x)=\lim_{x \rightarrow 2}\frac{3}{x^2-4}+1=\infty \\so\\x=2 \space is-vertical-as.\\lim_{x \rightarrow -2}f(x)=\lim_{x \rightarrow -2}\frac{3}{x^2-4}+1=\infty \\so\\x=-2 \space is-vertical-as.\] \[\lim_{x \rightarrow \pm \infty}\frac{3}{x^2-4}+1\rightarrow 0+1=1 \rightarrow y=1 \\is\\horizontal-as.\]
Saylilbaby
  • Saylilbaby
can u number em so I know what to put for each number @amoodarya
amoodarya
  • amoodarya
this operation was for finding asymptotes
amoodarya
  • amoodarya
to find intercept find the root(s) of f(x)=0 \[\frac{3}{x^2-4}+1=0\\\frac{3}{x^2-4}=-1\\x^2-4=-3\\x^2=1\\x=\pm1\]

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