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...
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?