# Graph y=-1/2*tan(3x)

Graph y=-1/2*tan(3x)
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 tangent function, , for equal to to find where the vertical asymptote occurs for .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Multiply .
Multiply and .
Multiply by .
Set the inside of the tangent function equal to .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Multiply .
Multiply and .
Multiply by .
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 .
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 .
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: where is an integer
Amplitude: None
Period:
Phase Shift: ( to the right)
Vertical Shift:
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### Name

Name one hundred eighty-four million five hundred forty-eight thousand seven hundred ninety-seven

### Interesting facts

• 184548797 has 4 divisors, whose sum is 190502016
• The reverse of 184548797 is 797845481
• Previous prime number is 31

### Basic properties

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

### Name

Name one billion six hundred sixty-nine million five hundred sixty-four thousand one hundred twenty-eight

### Interesting facts

• 1669564128 has 256 divisors, whose sum is 16953390720
• The reverse of 1669564128 is 8214659661
• Previous prime number is 347

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 48
• Digital Root 3

### Name

Name one billion nine hundred forty-four million five hundred seventy-three thousand six hundred seventy-two

### Interesting facts

• 1944573672 has 64 divisors, whose sum is 8753098464
• The reverse of 1944573672 is 2763754491
• Previous prime number is 4253

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 48
• Digital Root 3