# Graph 3sec(1/7x)

Graph 3sec(1/7x)
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 secant function, , for equal to to find where the vertical asymptote occurs for .
Solve for .
Multiply both sides of the equation by .
Simplify both sides of the equation.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify .
Multiply .
Multiply by .
Combine and .
Move the negative in front of the fraction.
Set the inside of the secant function equal to .
Solve for .
Multiply both sides of the equation by .
Simplify both sides of the equation.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Multiply .
Combine and .
Multiply by .
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.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
The vertical asymptotes for occur at , , and every , where is an integer. This is half of the period.
Secant 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 .
The period of the function can be calculated using .
Replace with in the formula for period.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Multiply 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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Multiply 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: where is an integer
Amplitude: None
Period:
Phase Shift: ( to the right)
Vertical Shift:
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### Name

Name two hundred ninety million eighty-eight thousand eight hundred ninety-nine

### Interesting facts

• 290088899 has 8 divisors, whose sum is 302203440
• The reverse of 290088899 is 998880092
• Previous prime number is 59

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 53
• Digital Root 8

### Name

Name one billion ninety-one million six hundred seventy thousand three hundred eighty-one

### Interesting facts

• 1091670381 has 8 divisors, whose sum is 1214831160
• The reverse of 1091670381 is 1830761901
• Previous prime number is 653

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 36
• Digital Root 9

### Name

Name one billion two hundred forty-six million five hundred thirty thousand six hundred seventy-seven

### Interesting facts

• 1246530677 has 16 divisors, whose sum is 1473994752
• The reverse of 1246530677 is 7760356421
• Previous prime number is 443

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 41
• Digital Root 5