5.4. Vertical Shift of Sinusoidal Functions http://www.ck12.org
2.f(x) = 3 ·sinx− 1
- First draw the horizontal sinusoidal axis and identify the five main points for the cosine wave. Be careful to note
that the amplitude is 2 and the cosine wave starts and ends at a low point because of the negative sign.
Practice
Graph each of the following functions that have undergone a vertical stretch, reflection, and/or a vertical shift.
1.f(x) =−2 sinx+ 4
2.g(x) =^12 cosx− 1
3.h(x) =3 sinx+ 2
4.j(x) =− 1 .5 cosx+^12
5.k(x) =^23 sinx− 3
Find the minimum and maximum values of each of the following functions.