# How do you graph y=-3tan(x-(pi/4)) over the interval [-pi, 2pi]?

Dec 8, 2014

A general tangent function has the form;

$y = A \tan \left(B x - C\right) + D$

$A$ changes the amplitude of the graph by stretching it in the vertical direction. $B$ changes the period of the graph by stretching it in the horizontal direction. $C$ tells you how far to move the graph in the $x$ direction, and $D$ tells you how far to move the graph in the $y$ direction.

First we should start with a basic tangent function. This is a graph of the function $y = \tan \left(x\right)$ on the interval $\left[- \pi , 2 \pi\right]$. Here $A$ and $B$ are $1$ and $C$ and $D$ are 0. Lets change the amplitude of our graph by including the $- 3$ from above. The negative will flip the image and the $3$ will stretch it vertically, so a graph of $- 3 \tan \left(x\right)$ would look like the red below. Now we can change the $C$ value to get our final graph. The $\frac{\pi}{4}$ term will move the graph $\frac{\pi}{4}$ radians to the right, so our final graph will look like the red below. 