The graph shown below depicts:
The graph shown below depicts:
Show Hint
- $y = \sec^{-1} x$
- $y = \sec x$
- $y = \csc^{-1} x$
- $y = \csc x$
The Correct Option is C
Solution and Explanation
Let's analyze the features of the graph shown:
- The graph has a range from $[0, \frac{\pi}{2}) \cup (\frac{\pi}{2}, \pi]$ and similar behavior mirrored across the X-axis (i.e., also in $[-\pi, -\frac{\pi}{2}) \cup (-\frac{\pi}{2}, 0]$), which corresponds to the principal values of the inverse cosecant function.
- The curve is defined for $|x| \geq 1$ and has vertical asymptotes at $x = -1$ and $x = 1$, which is consistent with $y = \csc^{-1} x$.
- The graph is not periodic, which rules out trigonometric functions like $\csc x$ or $\sec x$, which are periodic.
Therefore, this graph corresponds to the inverse cosecant function: $y = \csc^{-1} x$.
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