Questions: Graph the following function: (y=-frac52 sec (pi x+3 pi)) Step 1 of 2: Identify the shape of the more basic function that has been shifted, reflected, stretched or compressed.

Graph the following function: (y=-frac52 sec (pi x+3 pi)) Step 1 of 2: Identify the shape of the more basic function that has been shifted, reflected, stretched or compressed.
Transcript text: Graph the following function: $y=\frac{-5}{2} \sec (\pi x+3 \pi)$ Step 1 of 2: Identify the shape of the more basic function that has been shifted, reflected, stretched or compressed.
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Solution

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Solution Steps

Step 1: Identify the Basic Function

The given function is \( y = \frac{-5}{2} \sec (\pi x + 3\pi) \). The basic function here is the secant function, \( y = \sec(x) \).

Step 2: Transformations

The function \( y = \frac{-5}{2} \sec (\pi x + 3\pi) \) involves several transformations of the basic secant function:

  • Horizontal Stretch/Compression: The factor \(\pi\) inside the argument compresses the period of the secant function.
  • Horizontal Shift: The term \(3\pi\) shifts the function horizontally.
  • Vertical Stretch: The factor \(\frac{-5}{2}\) stretches the function vertically and reflects it across the x-axis.

Final Answer

The function \( y = \frac{-5}{2} \sec (\pi x + 3\pi) \) is a vertically stretched and reflected version of the basic secant function, with a horizontal compression and shift.

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