Tangent function transformations: horizontal compression, reflection, and translation

[aisha]

HOw does $$y-3=-\tan (-2x+\pi)$$ differ from $$y=tan(x)$$

$$y=-\tan [-2 (x+ \frac {\pi} {2} )] +3$$ rearranged

It differs because it has a

Horizontal compression by a factor of 1/2
it is reflected in the x and y-axis
there is a horizontal translation $$\frac {\pi} {2}$$ units to the left
and a vertical displacement 3 uinits up.

Can someone please tell me if I made any mistakes?

 

[HallsofIvy]

Looks like a good start.

 

[roger]

hallosivy, shouldn't that be -2(x-pi/2) instead of plus ?

 

[HallsofIvy]

Yep, sorry, didn't look close enough.