How do you graph $y = - 3 tan (x - (\frac{π}{4}))$ $y=-3tan(x-(pi/4))$ over the interval $[- π, 2 π]$ $[-pi, 2pi]$ ?

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How do you graph $y = - 3 tan (x - (\frac{π}{4}))$ $y=-3tan(x-(pi/4))$ over the interval $[- π, 2 π]$ $[-pi, 2pi]$ ?

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Answer 1 · 2014-12-08T03:41:44

A general tangent function has the form;

$y = A tan (B x - C) + D$ $y = Atan(Bx - C) + D$

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

First we should start with a basic tangent function. This is a graph of the function $y = tan (x)$ $y = tan(x)$ on the interval $[- π, 2 π]$ $[-pi,2pi]$ .

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Here $A$ $A$ and $B$ $B$ are $1$ $1$ and $C$ $C$ and $D$ $D$ are 0. Lets change the amplitude of our graph by including the $- 3$ $-3$ from above. The negative will flip the image and the $3$ $3$ will stretch it vertically, so a graph of $- 3 tan (x)$ $-3tan(x)$ would look like the red below.

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Now we can change the $C$ $C$ value to get our final graph. The $\frac{π}{4}$ $pi/4$ term will move the graph $\frac{π}{4}$ $pi/4$ radians to the right, so our final graph will look like the red below.

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How do you graph $y = - 3 tan (x - (\frac{π}{4}))$ $y=-3tan(x-(pi/4))$ over the interval $[- π, 2 π]$ $[-pi, 2pi]$ ?

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