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The secant function
f(x) = a*sec(bx+c)+d
and its properties such as period, phase shift, asymptotes domain and range are explored using an interactive applet by changing the parameters a, b, c and d. The figure below shows an example of the graph of this function.
Once you finish the present tutorial, you may want to go through a self test on trigonometric graphs .
Interactive Tutorial
Click on the button above "click here to start" and maximize the window obtained.
How do the 4 coefficients a,b,c and d affect the graph of f(x)?
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use the scrollbar to set a=1,b=1,c=0 and d=0. Write down f(x) and take note of the period, phase shift and positions of the asymptotes (in red) of f(x)? Now change a , how does it affect the graph?
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set a=1,c=0,d=0 and change b. Find the period from the graph and compare it to 2pi/|b|. How does b affect the graph of f(x)? How does it affect the asymptotes?
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set a=1,b=1,d=0 and change c starting from zero going slowly to positive large values. Take note of the shift, is it left or right, and compare it to -c/b.
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set a=1,b=1,d=0 and change c starting from zero going slowly to negative smaller values. Take note of the shift, is it left or right, and compare it to -c/b.
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repeat 3 and 4 above for b=2,3 and 4.
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set a,b and c to non zero values and change d. What is the direction of the shift of the graph?
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Which of the parameters affect the positions of the asymptotes(in red)? Explain analytically.
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Which of the parameters affect the domain of the secant function?
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Which of the parameters affect the range of the secant function?
More references on the trigonometric functions.
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