Graph y=tan(x)+2

Graph y=tan(x)+2
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 one hundred twenty-five million four hundred forty-two thousand five hundred eighty-five

Interesting facts

  • 125442585 has 8 divisors, whose sum is 132368128
  • The reverse of 125442585 is 585244521
  • Previous prime number is 31

Basic properties

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

Name

Name one billion forty-five million two hundred nineteen thousand ninety-six

Interesting facts

  • 1045219096 has 32 divisors, whose sum is 3528479880
  • The reverse of 1045219096 is 6909125401
  • Previous prime number is 4793

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 37
  • Digital Root 1

Name

Name two billion fifty-six million one hundred sixty-nine thousand six hundred fifty-nine

Interesting facts

  • 2056169659 has 8 divisors, whose sum is 2062645760
  • The reverse of 2056169659 is 9569616502
  • Previous prime number is 751

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 49
  • Digital Root 4