1. The problem involves understanding the general form of a sine function: $$y = A \sin(B(x - C)) + D$$ where: - $A$ is the amplitude (height of the wave peaks). - $B$ affects the period (frequency) of the wave. - $C$ is the horizontal shift (phase shift). - $D$ is the vertical shift. 2. The graph shows two sine waves: - A solid black sine wave with smaller amplitude and higher frequency. - A dashed blue sine wave with larger amplitude and lower frequency. 3. To add dotted lines (usually vertical or horizontal) to highlight key points like peaks, troughs, or intercepts, you can use equations of lines such as: - Vertical dotted lines at $x = k$ where $k$ is a specific $x$-value. - Horizontal dotted lines at $y = m$ where $m$ is a specific $y$-value. 4. For example, to add vertical dotted lines at $x = \frac{\pi}{2}$ and $x = \pi$, use: $$x = \frac{\pi}{2}, \quad x = \pi$$ 5. To add horizontal dotted lines at $y = 5$ and $y = -5$, use: $$y = 5, \quad y = -5$$ 6. These dotted lines help visualize the amplitude limits and key points on the graph. 7. Since the user asked for math dotted lines, the answer is to use equations of lines with dotted style in graphing software or plotting tools. Final answer: Use vertical dotted lines at $x = \frac{\pi}{2}, \pi, \ldots$ and horizontal dotted lines at $y = 5$ and $y = -5$ to highlight the sine wave features.