The graph of a trigonometric function is shown.

Question

The graph of a trigonometric function is shown. The graph has vertical asymptotes at multiples of pi. The graph alternates between upward-facing and downward-facing curves. The upward-facing curves decrease from infinity to y equals 1, then increase to infinity. The downward-facing curves increase from negative infinity to y equals negative 1, then decrease to negative infinity.
Question
Use the graph to answer the question.
Which function is shown in the graph?
(1 point)
Responses

y = tan θ
y = tan θ

y = sec θ
y = sec θ

y = csc θ
y = csc θ

y = cot θ
y = cot θ
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Answer 1

The description of the graph you provided suggests that the function has vertical asymptotes at multiples of π and alternates between upward-facing and downward-facing curves. This behavior is consistent with the function \( y = tan \theta \).

1. Vertical Asymptotes: The function \( y = tan \theta \) has vertical asymptotes at \( \theta = \frac{\pi}{2} + n\pi \) for integers \( n \), which corresponds to multiples of π.

2. Graph Behavior: The upward-facing curves of \( y = tan \theta \) go from negative infinity to positive infinity, and the downward-facing curves do the opposite. This behavior matches your description of how the values alternate.

Given this analysis, the function represented in the graph is most likely:

y = tan θ