Graph y=4tan(2x+135)

Graph y=4tan(2x+135)
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 .
Solve for .
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Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify each term.
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Multiply .
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Multiply and .
Multiply by .
Move the negative in front of the fraction.
Set the inside of the tangent function equal to .
Solve for .
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Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify each term.
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Multiply .
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Multiply and .
Multiply by .
Move the negative in front of the fraction.
The basic period for will occur at , where and are vertical asymptotes.
The absolute value is the distance between a number and zero. The distance between and is .
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 .
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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 .
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:
Move the negative in front of the fraction.
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 five million five hundred thirty-six thousand one hundred eighty-eight

Interesting facts

  • 205536188 has 128 divisors, whose sum is 600929280
  • The reverse of 205536188 is 881635502
  • Previous prime number is 23

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 38
  • Digital Root 2

Name

Name one billion twenty-four million three hundred ninety-one thousand eight hundred one

Interesting facts

  • 1024391801 has 4 divisors, whose sum is 1024620672
  • The reverse of 1024391801 is 1081934201
  • Previous prime number is 224303

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 29
  • Digital Root 2

Name

Name nine hundred thirty-two million three hundred thirty-two thousand nine hundred sixty-five

Interesting facts

  • 932332965 has 8 divisors, whose sum is 1491732768
  • The reverse of 932332965 is 569233239
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 42
  • Digital Root 6