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)?

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?

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?

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.

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.

repeat 3 and 4 above for b=2,3 and 4.

set a,b and c to non zero values and change d. What is the direction of the shift of the graph?

Which of the parameters affect the positions of the asymptotes(in red)? Explain analytically.

Which of the parameters affect the domain of the secant function?

Which of the parameters affect the range of the secant function?
More references on the trigonometric functions.

