Graph y=2sec(x)

Problem

y=2*sec(x)

Solution

1. Identify the parent function and its properties. The function y=2*sec(x) is a transformation of y=sec(x) which is the reciprocal of y=cos(x)

2. Determine the vertical stretch. The coefficient 2 indicates a vertical stretch by a factor of 2 This means the local minima of the curves will be at y=2 and the local maxima will be at y=−2

3. Locate the vertical asymptotes. Since sec(x)=1/cos(x) the function is undefined where cos(x)=0 This occurs at x=π/2+n*π for any integer n

4. Identify key points for one period. In the interval [0,2*π] the function has a local minimum at (0,2) a local maximum at (π,−2) and another local minimum at (2*π,2)

5. Sketch the curves. Draw the vertical asymptotes at x=−π/2 x=π/2 and x=(3*π)/2 Plot the key points and draw the U-shaped branches that approach the asymptotes.

Final Answer

y=2*sec(x)

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