## anonymous one year ago 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.

1. anonymous

$f(x)=\frac{ 3 }{ x^2-4 }+1$

2. amoodarya

what part of question ,is your problem ?

3. anonymous

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.

4. amoodarya

$vertical-retrice\rightarrow x^-4=0 \rightarrow x=\pm 2\\ \lim_{x \rightarrow 2}f(x)=\lim_{x \rightarrow 2}\frac{3}{x^2-4}+1=\infty \\so\\x=2 \space is-vertical-as.\\lim_{x \rightarrow -2}f(x)=\lim_{x \rightarrow -2}\frac{3}{x^2-4}+1=\infty \\so\\x=-2 \space is-vertical-as.$ $\lim_{x \rightarrow \pm \infty}\frac{3}{x^2-4}+1\rightarrow 0+1=1 \rightarrow y=1 \\is\\horizontal-as.$

5. anonymous

can u number em so I know what to put for each number @amoodarya

6. amoodarya

this operation was for finding asymptotes

7. amoodarya

to find intercept find the root(s) of f(x)=0 $\frac{3}{x^2-4}+1=0\\\frac{3}{x^2-4}=-1\\x^2-4=-3\\x^2=1\\x=\pm1$