# Graph y=tan(x-π/4) Include min, max, intercepts, and make sure you LABEL with points on the unit circle.

embizze | Certified Educator

Graph `y=tan(x-pi/4) ` :

This is the graph of y=tan(x) translated right `pi/4 ` units.

Thus the vertical asymptotes will be at `x=-pi/4+npi, n in ZZ ` (n an integer; i.e. the vertical asymptotes will occur at ` ``x=...,(-5pi)/4,-pi/4,(3pi)/4,... ` )

The x-intercepts will occur at `x=pi/4+npi,n in ZZ ` i.e. ` ``x=...,(-3pi)/4,pi/4,(5pi)/4,... `

The y-intercept is `y=tan(0-pi/4)=-1 `

There are no maximums or minimums.

The graph:

** The horizontal tick marks are in increments of `pi/4 ` .**

Some values:

x            `tan(x-pi/4) `
---         ---------------

0                    -1
`pi/6 `                  `tan(-pi/12)~~-.2679 `
`pi/4 `                    0
`pi/3 `                   `tan(pi/12)~~.2679 `
`pi/2 `                    1
`(2pi)/3 `                `tan((5pi)/12)~~3.7321 `
`(3pi)/4 `                 undefined
`(5pi)/6 `                `tan((7pi)/12)~~-3.7321 `
`pi `                  -1

etc...