Question

How do you graph `y=secpix`?

Answer 1

`sec (pix) = 1/cos(pi x)`

Explanation:

To graph any inverse function like this it is often easier to graph the normal function lightly and then draw the inverse over the top.

so for this graph `cos(pi*x)`

which goes through the y-axis at (0,1) has min at (1,-1) and max at (2,1)

with a period of 2. giving you a graph like this,

graph{cos(pix) [-2, 2, -4, 4]}

now let's look at some of the features of the graph and decide what will happen when we do `1/f(x)`.

1. any points where y=1 or y=-1 will remain the same
2. any points whey y=0 will become an asymptote
3. points at `y= 1/2` will go to`y=2`, points at `y=2` will go to `y = 1/2` ect.

now we can do a rough sketch of what the graph will look like.

graph{1/(cos(pix)) [-2, 2, -4, 4]}

It is easier to see the relationship if you superimpose them on one another