Question
1. (1 point) The graph shown is of the function a. y=tanx b. y=cotx c. y=-tanx d. y=-cotx
Solution
4
(219 Votes)
Quincy
Elite ยท Tutor for 8 years
Answer
To determine which function corresponds to the graph, we need to analyze the general behavior of the trigonometric functions provided in the options.### Key Characteristics of Each Function:1. **
:** - The tangent function has vertical asymptotes at
, where
is an integer. - It increases from negative infinity to positive infinity between consecutive asymptotes. - The graph passes through the origin (0, 0).2. **
:** - The cotangent function has vertical asymptotes at
, where
is an integer. - It decreases from positive infinity to negative infinity between consecutive asymptotes. - The graph does not pass through the origin but instead crosses the x-axis at
.3. **
:** - This is a reflection of
across the x-axis. - It has the same vertical asymptotes as
(
). - It decreases from positive infinity to negative infinity between consecutive asymptotes.4. **
:** - This is a reflection of
across the x-axis. - It has the same vertical asymptotes as
(
). - It increases from negative infinity to positive infinity between consecutive asymptotes.---### Steps to Identify the Graph:- Check the location of the vertical asymptotes: If they occur at
, it must be a tangent-related function (
or
). If they occur at
, it must be a cotangent-related function (
or
).- Determine whether the graph increases or decreases between asymptotes: - Increasing:
or
. - Decreasing:
or
.---### Final Answer:Without seeing the actual graph, you can use the above characteristics to match the correct function. For example:- If the graph has vertical asymptotes at
and decreases between them, the answer is **
**.- If the graph has vertical asymptotes at
and increases between them, the answer is **
**.Let me know if you have more details about the graph!