Question

sketch the graph: y = cot (pi/4 x). . well the period would be pi/b . - pi/ (pi/4 x). - I end up getting a period = 4. . HOW DO I FIND THE VERTICAL ASYMPTOTES?

Answer 1

Refer the attached figure.

Vertical asymptote
`x=4+4n`

Explanation:

Given : Function
`y=\cot ((\pi)/(4)x)`

To find : Sketch the given function and find the vertical asymptotes of the function ?

Solution :

Function
`y=\cot ((\pi)/(4)x)`

Sketch the function on the graph.

Refer the attached figure.

Now, Vertical asymptote is defined as

On a graph, a line which is approached by a curve but never reached.

i.e. on different values of x y tends to infinity.

When we see the graph the vertical asymptote of the function is given by

`x=4+4n` for n=0,1,2,3...

Answer 2

The general form of the equation is acot (bx−c)+d to find the variables used to find the amplitude, period, phase shift, and vertical shift where a=1, b=π/4, c=0 and d=0
Period is pi/b or equal to 4.

The vertical asymptote is 4pi n where n is integer.
Attached is the sketch of the graph