Answer
See graph and explanations.
Work Step by Step
a. As $x\to 0^+, y\to\infty$ because $\lim_{x\to 0^+}\frac{3}{2}(x-\frac{1}{x})^{2/3}=\frac{3}{2}\lim_{x\to 0^+}(\frac{1}{x})^{2/3}=\infty$;
b. As $x\to\pm\infty, y\to\infty$ because $\lim_{x\to\pm\infty}\frac{3}{2}(x-\frac{1}{x})^{2/3}=\lim_{x\to\pm\infty}\frac{3}{2}(x)^{2/3}=\infty$;
c. As $x\to 1, y\to0$ because $\lim_{x\to 1}\frac{3}{2}(x-\frac{1}{x})^{2/3}=\frac{3}{2}(1-\frac{1}{1})^{2/3}=0$;
Similarly, As $x\to -1, y\to0$ because $\lim_{x\to -1}\frac{3}{2}(x-\frac{1}{x})^{2/3}=\frac{3}{2}(-1+\frac{1}{1})^{2/3}=0$;
