Graph y=2sec(x)

Graph y=2sec(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 secant function, , for equal to to find where the vertical asymptote occurs for .
Set the inside of the secant 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. Vertical asymptotes occur every half period.
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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. This is half of the period.
There are only vertical asymptotes for secant and cosecant 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 billion eight hundred twenty-four million one hundred fifty-four thousand two hundred ninety-six

Interesting facts

  • 1824154296 has 64 divisors, whose sum is 8211611520
  • The reverse of 1824154296 is 6924514281
  • Previous prime number is 3191

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 42
  • Digital Root 6

Name

Name one billion seven hundred fifty-four million five hundred thirty-four thousand six hundred fifty-two

Interesting facts

  • 1754534652 has 64 divisors, whose sum is 4193925120
  • The reverse of 1754534652 is 2564354571
  • Previous prime number is 461

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 42
  • Digital Root 6

Name

Name three hundred twenty million nine hundred thirty-nine thousand four hundred eighteen

Interesting facts

  • 320939418 has 16 divisors, whose sum is 648235296
  • The reverse of 320939418 is 814939023
  • Previous prime number is 101

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 39
  • Digital Root 3