Answer
The $x$-intercepts: $(-4,0)$ and $(4,0)$
Work Step by Step
(a) Using a graphing utility, the graph of the function is as shown. The $x$-intercepts shown are $(-4,0)$ and $(4,0)$.
(b) Setting $y=0$:
$$0=x-\frac{16}{x}$$ $$0=\frac{x^2-16}{x}$$ $$0=x^2-16$$ $$x^2=16$$ $$x=\pm\sqrt{16}$$ $$x=\pm4$$ $$x_1=-4$$ $$x_2=4$$
Thus, the resulting equation is $x=-4$ and $x=4$, and the result in part (a) is confirmed.
