Question

Choose the graph of y = 2 tan x.

Answer 1

Find the asymptotes

For any y=tan(x), vertical asymptotes occur at x = $\frac{\pi }{2}$ + $n\pi$, where $n$ is an integer.

Use the basic period for y=tan(x), $(-\frac{\pi }2} , \frac{\pi }{2} )$, to find the vertial asymptotes for y= 2 tan (x). Set the inside of the tangent function, bx+c, for y = a tan (bx+c) + d equal to -$\frac{\pi }{2}$ to find where the vertical asymptote occurs for y=2tan(x).

$x=-\frac{\pi }{2}$

Set the inside of the tangent function x equal to $\frac{\pi }{2}$

x=$\pi /2$

the basic period for y=2tan(x) will occur at (-$\pi/2 ,\pi /2$), where -pi/2 and pi/2 are vertical asymptotes.

$(-\frac{\pi }{2} , \frac{\pi }{2} )$

Find the period $\frac{\pi }{|b|}$ to find where the vertical asymptotes exist.

The absolute value is the distance between a number and zero. The distance between 0 and 1 is 1.

$\frac{\pi }{1}$

Divide $\pi$ by 1

$\pi$

The vertical asymptotes for y = 2 tan (x)  occur at $-\frac{\pi }{2} , \frac{\pi }{2,}$ and every $\pi n$, and where n is a integer.

$\pi n$

There are only vertical asymptotes for tangent and contagent functions.

Vertical asymptotes : $x=\frac{\pi }{2} +\pi n$  for any integer n.

No horizontal asymptotes

No oblique asymptotes

use a form for a tan (bx-c)+d to find variables used to find the amptitude , period, phase shift, and vertical shift.

a=2

b=1

c=0

d=0

Since the graph of the function tan does not have a maximum or minimum value, there can be no value for amplitude.

Amplitude : None

Find the period of 2 tan (x)

The period of the function can be caculated using $\frac{\pi }{|b|}$

$\pi /|b|$

Replace b with 1 in the formula for period.

$\frac{\pi }{|1|}$

The absolute value is the distance between a number and zero . The distance between 0 and 1 is 1.

$\frac{\pi }{1}$

Divide $\pi$ by 1

$\pi$

Find the phase shift using the formula $\frac{c}{b}$

Phase Shift: $\frac{c}{b}$

Replace the values of c and b in the equation for phase shift

Phase shift: 0/1

Divide 0 by 1

Phase Shift; 0

Find the vertical shift d.

vertical shift: 0

List the properties of the trigonometric function

Amplitude; none

period: $\pi$

Phase shift: 0 ( 0 to right )

Vertical shift: 0

The trig function can be graphed using the amplitude , period, phase shift, vertical shift, and the points.

Vertical asymptotes : x= pi/2+pi n for any integer n.

Amplitude: None

Period: $\pi$

Phase Shift: 0 ( 0 to the right)

Vertical Shift: 0

Answer 2

Answer:

The image shows the graph of y = 2 tan x.