Graph y=-4sec(x)

Problem

y=−4*sec(x)

Solution

1. Identify the parent function and its properties. The function y=sec(x) is the reciprocal of cos(x) meaning it has vertical asymptotes where cos(x)=0 which occurs at x=π/2+n*π

2. Determine the vertical stretch and reflection. The coefficient −4 indicates a vertical stretch by a factor of 4 and a reflection across the xaxis.

3. Locate the relative extrema of the curves. In the parent function y=sec(x) the local minima are at (2*n*π,1) and local maxima are at ((2*n+1)*π,−1) Due to the −4 multiplier, these points shift to (2*n*π,−4) and ((2*n+1)*π,4)

4. Identify the asymptotes, which remain unchanged from the parent function. Vertical asymptotes occur at x=−π/2 x=π/2 x=(3*π)/2 etc.

5. Sketch the curves between the asymptotes. Instead of U-shaped curves opening up from y=1 the reflected and stretched curves open down from y=−4 and up from y=4

Final Answer

y=−4*sec(x)

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