How do you find the amplitude, period, and shift for #y=4tan(2x-pi)#?

1 Answer
Mar 17, 2016

The amplitude is 4, the period is #pi/2#, and the graph is shifted to the right #pi/2#.

Explanation:

The general pattern for a tangent function is:
#y=atanb(x-h)+k#

In this case, #a# is 4, so the amplitude is 4.

To find the period, we need to find the #b# value first. To do this, we need to pull out the 2 in order to isolate #x#. Therefore, we get:
#y=4tan2(x-pi/2)#
The period for a tangent function is equal to #pi/b#.
#pi/b=pi/2#

The #h# value is how much the graph is shifted horizontally. In this case, we can see that the graph is shifted to the right #pi/2#.