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Magazine Problem 46
Sketch the graph of the equation. Use intercepts, extrema, and asymptotes as sketching aids. \(g(x)=\frac{x}{x^{2}-4}\)
Problem 47
Sketch the graph of the equation. Use intercepts, extrema, and asymptotes as sketching aids. \(x y^{2}=4\)
Problem 48
Sketch the graph of the equation. Use intercepts, extrema, and asymptotes as sketching aids. \(x^{2} y=4\)
Problem 49
Sketch the graph of the equation. Use intercepts, extrema, and asymptotes as sketching aids. \(y=\frac{2 x}{1-x}\)
Problem 50
Sketch the graph of the equation. Use intercepts, extrema, and asymptotes as sketching aids. \(y=\frac{2 x}{1-x^{2}}\)
Problem 51
Sketch a graph of a function \(f\) having the given characteristics. (There are
many correct answers.)
$$
\begin{aligned}
&f(-2)=f(0)=0 \\
&f^{\prime}(x)>0 \text { if } x<-1 \\
&f^{\prime}(x)<0 \text { if }-1
Problem 51
Sketch the graph of the equation. Use intercepts, extrema, and asymptotes as sketching aids. \(y=1-3 x^{-2}\)
Problem 52
Sketch a graph of a function \(f\) having the given characteristics. (There are many correct answers.) $$ \begin{aligned} &f(-1)=f(3)=0\\\ &f^{\prime}(1) \text { is undefined. }\\\ &f^{\prime}(x)<0 \text { if } x<1\\\ &f^{\prime}(x)>0 \text { if } x>1\\\ &f^{\prime \prime}(x)<0, x \neq 1\\\ &\lim _{x \rightarrow \infty} f(x)=4 \end{aligned} $$
Problem 52
Sketch the graph of the equation. Use intercepts, extrema, and asymptotes as sketching aids. \(y=1+x^{-1}\)
Problem 53
Sketch the graph of the equation. Use intercepts, extrema, and asymptotes as sketching aids. \(f(x)=\frac{1}{x^{2}-x-2}\)
