College Algebra & Trigonometry, 2018a

9.5. COMBINING THE TRANSFORMATIONS 429
Again, notice that the distance along the x-axis from the starting point to the
ending point is the period: 2π 3
. Now let’s graph the function:
−2
π
3
π
2
2π
3
5π
6
π
−4
or
−1.5
−2.5
−3.5
π
3
π
2
2π
3
5π
6
π
Let’s look at one more example.
Example 3
Sometimes the coefficient B appears factored out of the argument as it does in
the problem below.
Graph at least one period of the given function. Be sure to include the critical
values along the x and y axes.
y =4sin2(x+ π 3 ) − 1.
First let’s see how the x and y axes are affected by the transformations in this
problem.