# Graph 4(tan(x))

Graph 4(tan(x))
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 .
Set the inside of the tangent function equal to .
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.
There are only vertical asymptotes for tangent and cotangent functions.
Vertical Asymptotes: for any integer
No Horizontal Asymptotes
No Oblique Asymptotes
Vertical Asymptotes: for any integer
No Horizontal Asymptotes
No Oblique Asymptotes
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 right)
Vertical Shift:
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Vertical Asymptotes: for any integer
Amplitude: None
Period:
Phase Shift: ( to the right)
Vertical Shift:
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### Name

Name two billion one hundred twelve million four hundred twenty-nine thousand one hundred sixty-seven

### Interesting facts

• 2112429167 has 4 divisors, whose sum is 2127848496
• The reverse of 2112429167 is 7619242112
• Previous prime number is 137

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 35
• Digital Root 8

### Name

Name one billion one hundred seventeen million forty-seven thousand four hundred fifty-three

### Interesting facts

• 1117047453 has 8 divisors, whose sum is 1494096288
• The reverse of 1117047453 is 3547407111
• Previous prime number is 317

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 33
• Digital Root 6

### Name

Name one hundred thirty-eight million three hundred fifty-four thousand five hundred eleven

### Interesting facts

• 138354511 has 4 divisors, whose sum is 141298272
• The reverse of 138354511 is 115453831
• Previous prime number is 47

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 31
• Digital Root 4