# Characteristics of y=tan(x)

• Jun 9th 2011, 11:06 AM
starshine84
Characteristics of y=tan(x)
I need to state domain, range, period, vertical asymptotes, zeros, symmetry and y-intercept of y = -2tan (3x + 180) +3.

I just finished doing the same for y = sin(x) and y=cos(x) and I know these shouldn't be much harder, but I'm having difficulty figuring out how to find the domain and range to begin with.

I know that it needs to be factored first:
y = -2tan (3x + 180) +3
y = -2tan (3 (x + 60)) + 3
y = -2tan (3 (x - (-60))) + 3

I know that -2 is the vertical stretch and also tells me that the function is reflected in the x-axis. I know that the 3 means that it is compressed horizontally by a factor of 1/3. I believe the 60 means that it is shifted 60 degrees to the right. I also know that the last 3 means that it has been shifted three units up.

From here, I'm not sure what to do though...
• Jun 9th 2011, 04:49 PM
Sudharaka
Quote:

Originally Posted by starshine84
I need to state domain, range, period, vertical asymptotes, zeros, symmetry and y-intercept of y = -2tan (3x + 180) +3.

I just finished doing the same for y = sin(x) and y=cos(x) and I know these shouldn't be much harder, but I'm having difficulty figuring out how to find the domain and range to begin with.

I know that it needs to be factored first:
y = -2tan (3x + 180) +3
y = -2tan (3 (x + 60)) + 3
y = -2tan (3 (x - (-60))) + 3

I know that -2 is the vertical stretch and also tells me that the function is reflected in the x-axis. I know that the 3 means that it is compressed horizontally by a factor of 1/3. I believe the 60 means that it is shifted 60 degrees to the right. I also know that the last 3 means that it has been shifted three units up.

From here, I'm not sure what to do though...

Dear starshine84,

You should realize that if the given angles are measured in degrees, \$\displaystyle \tan(3x+180)=\tan{3x}\$

Hence, \$\displaystyle y=-2\tan(3x+180)+3=-2\tan{3x}+3\$

Now you could easily sketch the graph and find out the answers.

Hope you can continue.
• Jun 13th 2011, 04:12 AM
starshine84
I'm a little confused about what you did there.... how does tan (3x + 180) = tan 3x? That has not been taught in my course :S

For the sin and cos functions there were ways to find each of the characteristics from equations themselves. There is no way to do that for the tan function?
• Jun 13th 2011, 12:29 PM
mr fantastic
Re: Characteristics of y=tan(x)
Quote:

Originally Posted by starshine84
I'm a little confused about what you did there.... how does tan (3x + 180) = tan 3x? That has not been taught in my course :S

For the sin and cos functions there were ways to find each of the characteristics from equations themselves. There is no way to do that for the tan function?

The period of tan(A) is 180 degrees. So tan(A + 180) = tan(A).