Answer:
a) [tex]G(x)= \sin x + 2[/tex]
b) The coordinates of P are
[tex]\displaystyle \left( \frac{3\pi}{2},1\right)[/tex]
Step-by-step explanation:
Translation
The dashed line shows the graph of the function
[tex]y = \sin x[/tex]
This function has a maximum value of 1, a minimum value of -1, and a center value of 0.
a)
Graph G shows the same function but translated by 2 units up, thus the equation of G is:
[tex]\boxed{G(x)= \sin x + 2}[/tex]
b) The coordinates of P correspond to the value of
[tex]x = \frac{3\pi}{2}[/tex]
The value of G is
[tex]\displaystyle G(\frac{3\pi}{2})= \sin \frac{3\pi}{2} + 2[/tex]
Since
[tex]\sin \frac{3\pi}{2}=-1[/tex]
[tex]\displaystyle G(\frac{3\pi}{2})= -1+ 2=1[/tex]
The coordinates of P are
[tex]\displaystyle \left( \frac{3\pi}{2},1\right)[/tex]
