Graph y=(1/2)tan(x)

Graph y=(1/2)tan(x)
Find the asymptotes.
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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.
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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 .
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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 .
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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 four hundred twenty-two million six hundred forty thousand seven hundred forty-seven

Interesting facts

  • 422640747 has 8 divisors, whose sum is 584392256
  • The reverse of 422640747 is 747046224
  • Previous prime number is 27

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 36
  • Digital Root 9

Name

Name one billion six hundred fifty-one million eight hundred ninety-one thousand forty

Interesting facts

  • 1651891040 has 512 divisors, whose sum is 15658920000
  • The reverse of 1651891040 is 0401981561
  • Previous prime number is 199

Basic properties

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

Name

Name four hundred thirty-two million thirty-seven thousand four hundred

Interesting facts

  • 432037400 has 64 divisors, whose sum is 1520515152
  • The reverse of 432037400 is 004730234
  • Previous prime number is 401

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 23
  • Digital Root 5