In Exercises 39-48, use a graphing utility to graph the function. Include two full periods. $y=-tan2x$

Step by Step Solution: Step 1. To graph the function $y=-tan(2x)$, we first need to identify the properties of the tangent function. Step 2. The tangent function has a vertical asymptote at every odd multiple of $\frac{\pi }{2}$ and a period of $\pi$. Step 3. The negative sign in the function reflects the graph about the x-axis. Step 4. To graph two full periods, we can graph the function over the interval $x\in [0,\pi ]$, then replicate that interval to the right and left of the initial interval. Step 5. Creating a table of values by selecting values for $x$ and calculating the corresponding values for $y$, we get: Step 6. | $x$ | $-tan(2x)$ | Step 7. |---|---| Step 8. | $0$ | $0$ | Step 9. | $\frac{\pi }{6}$ | $\sqrt{3}$ | Step 10. | $\frac{\pi }{4}$ | $1$ | Step 11. | $\frac{\pi }{3}$ | $-\sqrt{3}$ | Step 12. | $\frac{\pi }{2}$ | undefined | Step 13. | $\frac{2\pi }{3}$ | $\sqrt{3}$ | Step 14. | $\frac{3\pi }{4}$ | $-1$ | Step 15. | $\frac{5\pi }{6}$ | $\sqrt{3}$ | Step 16. | $\pi$ | $0$ | Step 17. Using these points, we can sketch the graph of the function. Step 18. Since the period of $y=-tan(2x)$ is $\frac{\pi }{2}$, we can replicate the graph from $x=0$ to $x=\frac{\pi }{2}$ to get two full periods of the graph. Step 19. The graph of $y=-tan(2x)$ with two full periods is shown below: