**Text:** The function graphed is of the form \( y = a \sec(bx) \) or \( y = a \csc(bx) \), where \( b > 0 \). Determine the equation of the graph. **Graph Explanation:** The graph shows two segments of an upward-opening curve and one downward-opening curve, consistent with the behavior of a secant function. These curves intersect the \( y \)-axis and have vertical asymptotes where the function is undefined. - The \( x \)-axis is labeled with key points at \(-\frac{\pi}{2}\), \(-\frac{\pi}{4}\), \(0\), \(\frac{\pi}{4}\), and \(\frac{\pi}{2}\). - The \( y \)-axis is labeled with integers from \(-6\) to \(6\), indicating the range on the graph. - Vertical asymptotes are visible at \( x = -\frac{\pi}{2} \), \( x = 0 \), and \( x = \frac{\pi}{2} \). - The curves pass through \( (0, 1) \) and appear symmetric about the \( y \)-axis, which suggests the usage of a secant function. Given these observations, \( b \) in the functions \( \sec(bx) \) or \( \csc(bx) \) would be calculated to match the period \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\), implying a full period of \(\pi\). Hence, \( b = 2 \), and the equation is likely \( y = \sec(2x) \). The image shows a graph with both x and y axes. The graph depicts a periodic function, likely the cosine function. **Axes Description:** - The x-axis is labeled "x" with tick marks at \(-\frac{\pi}{2}\), \(-\frac{\pi}{4}\), \(0\), \(\frac{\pi}{4}\), and \(\frac{\pi}{2}\). - The y-axis is labeled "y" with tick marks at intervals of 2, ranging from -6 to 6. **Function Description:** - The function appears to have the shape of an inverted cosine curve. There are two full cycles shown between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\). - The maximum points of the curves appear at the y-values of 6, while the minima hit -6. This graph is likely used to illustrate the periodic nature and properties of cosine or a similar trigonometric function, such as plotting transformations or examining amplitude and frequency changes.

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