Graph y=1/2*sec(x)

Problem

y=1/2*sec(x)

Solution

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

2. Determine the vertical stretch. The coefficient 1/2 indicates a vertical compression by a factor of 2 The local minima of the secant curves will be at y=1/2 and the local maxima will be at y=−1/2

3. Find the period. Since there is no horizontal stretch or compression (the coefficient of x is 1, the period remains 2*π

4. Locate the vertical asymptotes. The function y=sec(x) is undefined where cos(x)=0 These vertical asymptotes occur at x=π/2+n*π for any integer n

5. Plot key points within one period. For x=0 y=1/2*sec(0)=1/2 For x=π y=1/2*sec(π)=−1/2

6. Sketch the curves. Draw U-shaped branches that approach the vertical asymptotes, starting from the local extrema at (0,1/2) and (π,−1/2)

Final Answer

y=1/2*sec(x)

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