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## Homework Statement

Graph ##y=tan\left(x-\frac {π}{4}\right)##

## Homework Equations

N/A

## The Attempt at a Solution

To graph a tangent function, I first find the vertical asymptotes to set the boundaries for the graph:

To do so, set what's inside the parentheses equal to ##\frac π 2## and ##-\frac π 2## and solve. This gives me the vertical asymptotes of ##\frac {3π}{4}## and ##-\frac π 4##.

Next, I divide the x-axis into 4 equal intervals:

Period= ##\frac π b## = ##\frac π 1## = π, since the b value of the function is 1.

Next, I evaluate the function at the three found x-values:

##y=tan\left(\frac π 4 - \frac π 4\right)## = 0

##y=tan\left(\frac π 2 - \frac π 4\right)## = ##tan\left(\frac π 4\right)=1##

##y=tan\left(\frac {3π}{4} - \frac π 4\right)## = ##tan\left(\frac π 2\right)## = UNDEFINED

Now here is my trouble- In looking at the original graph, the tangent function is shifted to the right by ##\frac π 4## units. This should also mean that the vertical asymptotes shift as well, while keeping their same interval value. So the graph of the given function is not undefined at ##\frac π 2## like a basic tangent function graph. However, I still need another acceptable x value so that I can draw the graph. But my third value is undefined.

Any ideas on where I'm going wrong?