Question 500174: Please answer and graph the amplitude, period, increments, asymptotes, and whether or not there are shifts or reflections of y= secant(piX-1)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Please answer and graph the amplitude, period, increments, asymptotes, and whether or not there are shifts or reflections of y= secant(piX-1)
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Equation for secant function: y=sec(Bx-C), period=2π/B, phase shift=C/B
For given secant function: y=sec(πx-1)
B=π
period=2π/B=2π/π=2
phase shift=C/B=1/π=.3183 (to the right)
Graph for one period:
First, draw the secant curve with no phase shift plotting the following points on an (x,y) coordinate system:
(0,1), (1,-1),and (2,1)
Asymptotes: x=.5, 1.5, and 2
..
To draw given secant function, shift all the x-coordinates .3183 units to the right, giving the following:
(.3183,1), (1.3183,-1),and (2.3183,1)
Asymptotes: x=.8183, 1.8183, and 2.8183
To complete the graph, extend the curve back to the y-axis, where x=1.8502 (y-intercept)
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