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The given graph shows a function that looks like a secant or cosecant function, based on the vertical asymptotes and the general shape of the curve. Let's analyze it step by step:

### Observations:
- There are vertical asymptotes at \( x = -\frac{\pi}{2} \) and \( x = \frac{\pi}{2} \), which is a common feature of the secant or cosecant functions.
- The shape between the asymptotes is an upward-opening curve, which resembles the secant function, as the basic secant function \( y = \sec(x) \) has similar behavior.
  
### Function form:
The general form given is either:
- \( y = a \sec(bx) + c \), or
- \( y = a \csc(bx) + c \).

From the graph:
- The asymptotes indicate a period of \( \pi \). In the secant function \( y = \sec(bx) \), the period is \( \frac{2\pi}{b} \). Since the period here is \( \pi \), we set \( b = 2 \).
- The secant function's basic graph has an upward curve between asymptotes and looks like the one presented. This confirms we are dealing with a secant function.
- The graph is symmetric around the y-axis, and the vertical shift appears to be zero, so \( c = 0 \).

Now, to determine the amplitude:
- From the graph, the curve reaches a maximum of 10 and a minimum of -10, suggesting \( a = 10 \).

### Final Equation:
The equation of the function is:
\[
y = 10 \sec(2x)
\]

Would you like more details, or do you have any questions? Here are some related questions to consider:

1. How does the period of a secant function depend on the value of \( b \)?
2. What are the key differences between secant and cosecant graphs?
3. How do vertical asymptotes help determine the form of trigonometric functions?
4. What role does the amplitude \( a \) play in the graph of a secant function?
5. How can we shift the secant function vertically or horizontally?

**Tip:** For secant functions, remember that their vertical asymptotes occur where the corresponding cosine function equals zero.

The function graphed to the right is of the form y = a sec(bx) + c or y = a csc(bx) + c for some a ≠ 0, b > 0. Determine the equation of the function.

Learn how to determine the equation of a secant function from a graph with vertical asymptotes at ±π/2 and an amplitude of 10. Explore key trigonometric concepts such as secant functions, vertical asymptotes, and periodicity. Suitable for students in Grades 10-12.

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