# Graph y=2tan(x+3)

Graph y=2tan(x+3)
Find the asymptotes.
For any , vertical asymptotes occur at , where is an integer. Use the basic period for , , to find the vertical asymptotes for . Set the inside of the tangent function, , for equal to to find where the vertical asymptote occurs for .
Subtract from both sides of the equation.
Set the inside of the tangent function equal to .
Subtract from both sides of the equation.
The basic period for will occur at , where and are vertical asymptotes.
Find the period to find where the vertical asymptotes exist.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The vertical asymptotes for occur at , , and every , where is an integer.
Tangent only has vertical asymptotes.
No Horizontal Asymptotes
No Oblique Asymptotes
Vertical Asymptotes: where is an integer
No Horizontal Asymptotes
No Oblique Asymptotes
Vertical Asymptotes: where is an integer
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Since the graph of the function does not have a maximum or minimum value, there can be no value for the amplitude.
Amplitude: None
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
Find the phase shift using the formula .
The phase shift of the function can be calculated from .
Phase Shift:
Replace the values of and in the equation for phase shift.
Phase Shift:
Divide by .
Phase Shift:
Phase Shift:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude: None
Period:
Phase Shift: ( to the left)
Vertical Shift:
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Vertical Asymptotes: where is an integer
Amplitude: None
Period:
Phase Shift: ( to the left)
Vertical Shift:
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### Name

Name two hundred eighty-eight million twenty thousand four hundred thirty-one

### Interesting facts

• 288020431 has 8 divisors, whose sum is 298314720
• The reverse of 288020431 is 134020882
• Previous prime number is 887

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 28
• Digital Root 1

### Name

Name seven hundred twenty-two million three hundred thirty-five thousand one hundred forty-eight

### Interesting facts

• 722335148 has 32 divisors, whose sum is 1700275104
• The reverse of 722335148 is 841533227
• Previous prime number is 397

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 35
• Digital Root 8

### Name

Name one billion seven hundred eighty-eight million seventy-two thousand five hundred ninety-four

### Interesting facts

• 1788072594 has 64 divisors, whose sum is 4465428480
• The reverse of 1788072594 is 4952708871
• Previous prime number is 743

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 51
• Digital Root 6