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Graph the function on a graphing calculator on the window \(x=[-5,5]\) and estimate the horizontal asymptote or limit. Then, calculate the actual horizontal asymptote or limit. \(f(x)=\frac{1}{x+10}\)

For the following exercises, graph the function on a graphing calculator on the window \(x=[-5,5]\) and estimate the horizontal asymptote or limit. Then, calculate the actual horizontal asymptote or limit. $$ f(x)=\frac{x+1}{x^{2}+7 x+6} $$

Graph the function on a graphing calculator on the window \(x=[-5,5]\) and estimate the horizontal asymptote or limit. Then, calculate the actual horizontal asymptote or limit. \(f(x)=\frac{x+1}{x^{2}+7 x+6}\)

For the following exercises, graph the function on a graphing calculator on the window \(x=[-5,5]\) and estimate the horizontal asymptote or limit. Then, calculate the actual horizontal asymptote or limit. $$ \lim _{x \rightarrow-\infty} x^{2}+10 x+25 $$

Graph the function on a graphing calculator on the window \(x=[-5,5]\) and estimate the horizontal asymptote or limit. Then, calculate the actual horizontal asymptote or limit. \(\lim _{x \rightarrow-\infty} x^{2}+10 x+25\)

Graph the function on a graphing calculator on the window \(x=[-5,5]\) and estimate the horizontal asymptote or limit. Then, calculate the actual horizontal asymptote or limit. \(\lim _{x \rightarrow-\infty} \frac{x+2}{x^{2}+7 x+6}\)

For the following exercises, graph the function on a graphing calculator on the window \(x=[-5,5]\) and estimate the horizontal asymptote or limit. Then, calculate the actual horizontal asymptote or limit. $$ \lim _{x \rightarrow-\infty} \frac{x+2}{x^{2}+7 x+6} $$

Graph the function on a graphing calculator on the window \(x=[-5,5]\) and estimate the horizontal asymptote or limit. Then, calculate the actual horizontal asymptote or limit. \(\lim _{x \rightarrow \infty} \frac{3 x+2}{x+5}\)

For the following exercises, graph the function on a graphing calculator on the window \(x=[-5,5]\) and estimate the horizontal asymptote or limit. Then, calculate the actual horizontal asymptote or limit. $$ \lim _{x \rightarrow \infty} \frac{3 x+2}{x+5} $$

Draw a graph of the functions without using a calculator. Be sure to notice all important features of the graph: local maxima and minima, inflection points, and asymptotic behavior. \(y=3 x^{2}+2 x+4\)