Q3. Given the function :

• What is the stretching factor?

• What is the period? (Type pi for , if needed.)

• Where are the asymptotes? Enter a list of values, separated by commas. Type pi for , as needed.

Background

Topic: Graphs and Properties of Trigonometric Functions (Secant Function)

This question tests your understanding of how to analyze and graph a transformed secant function, including identifying the stretching factor, period, and vertical asymptotes.

Key Terms and Formulas

• Secant Function:

• General Form:

• Stretching Factor: The value of stretches or compresses the graph vertically.

• Period of Secant:

• Vertical Asymptotes: Occur where (since is undefined there).

Step-by-Step Guidance

1. Identify the stretching factor by looking at the coefficient in . Here, .

2. Determine the period using the formula , where is the coefficient of inside the secant function. In this case, .

3. Set up the equation for the period: .

4. To find the vertical asymptotes, solve . Recall that at , where is any integer.

5. Set and solve for to find the locations of the asymptotes.

Try solving on your own before revealing the answer!