1. (1 point) The graph shown is of the function a. y=tanx b. y=cotx c. y=-tanx d. y=-cotx

To determine which function corresponds to the graph, we need to analyze the general behavior of the trigonometric functions provided in the options.<br /><br />### Key Characteristics of Each Function:<br />1. **\( y = \tan x \):**<br /> - The tangent function has vertical asymptotes at \( x = \frac{\pi}{2} + n\pi \), where \( n \) is an integer.<br /> - It increases from negative infinity to positive infinity between consecutive asymptotes.<br /> - The graph passes through the origin (0, 0).<br /><br />2. **\( y = \cot x \):**<br /> - The cotangent function has vertical asymptotes at \( x = n\pi \), where \( n \) is an integer.<br /> - It decreases from positive infinity to negative infinity between consecutive asymptotes.<br /> - The graph does not pass through the origin but instead crosses the x-axis at \( x = \frac{\pi}{2} + n\pi \).<br /><br />3. **\( y = -\tan x \):**<br /> - This is a reflection of \( y = \tan x \) across the x-axis.<br /> - It has the same vertical asymptotes as \( y = \tan x \) (\( x = \frac{\pi}{2} + n\pi \)).<br /> - It decreases from positive infinity to negative infinity between consecutive asymptotes.<br /><br />4. **\( y = -\cot x \):**<br /> - This is a reflection of \( y = \cot x \) across the x-axis.<br /> - It has the same vertical asymptotes as \( y = \cot x \) (\( x = n\pi \)).<br /> - It increases from negative infinity to positive infinity between consecutive asymptotes.<br /><br />---<br /><br />### Steps to Identify the Graph:<br />- Check the location of the vertical asymptotes: If they occur at \( x = \frac{\pi}{2} + n\pi \), it must be a tangent-related function (\( \tan x \) or \( -\tan x \)). If they occur at \( x = n\pi \), it must be a cotangent-related function (\( \cot x \) or \( -\cot x \)).<br />- Determine whether the graph increases or decreases between asymptotes:<br /> - Increasing: \( \tan x \) or \( -\cot x \).<br /> - Decreasing: \( -\tan x \) or \( \cot x \).<br /><br />---<br /><br />### Final Answer:<br />Without seeing the actual graph, you can use the above characteristics to match the correct function. For example:<br />- If the graph has vertical asymptotes at \( x = \frac{\pi}{2} + n\pi \) and decreases between them, the answer is **\( y = -\tan x \)**.<br />- If the graph has vertical asymptotes at \( x = n\pi \) and increases between them, the answer is **\( y = -\cot x \)**.<br /><br />Let me know if you have more details about the graph!