College Algebra & Trigonometry, 2018a

9.5. COMBINING THE TRANSFORMATIONS 431
To find the rest of the critical values we’ll need to add π 4
to the starting point of
the graph (− π 3 ) four times: − π 3 +π 4 =−4π
12 +3π 12 =− π 12
− π 12 +3π 12 =2π 12 =π 6
2π
12 +3π 12 =5π 12
5π
12 +3π 12 =8π 12 =2π 3
So the critical values along the x-axis would be:
− 4π
12 , −1π 12 , 2π
12 , 5π
12
or
, and
8π
12
− π 3 , − π 12 , π 6 , 5π
12 , and 2π 3
Now that we’ve addressed each of the four transformations let’s use this information
to draw the graph. First the y-axis - the amplitude is 4 and the vertical
shift is −1:
3
−1
−5