Question

In what direction and by how many units is the graph of f(x) = −7 sin(3x + π) − 2 vertically and horizontally shifted?

Answer 1

@wwhitlock

Answer 2

Hint:
\[\Large f(x) = -7\sin\left(3x+\pi\right)-2\]
can be written as
\[\Large f(x) = -7\sin\left(3\left(x+\frac{\pi}{3}\right)\right)+(-2)\]
which turns into
\[\Large f(x) = -7\sin\left(3\left(x-\left(-\frac{\pi}{3}\right)\right)\right)+(-2)\]

Answer 3

From here, notice how
\[\Large f(x) = {\color{red}{-7}}\sin\left({\color{blue}{3}}\left(x-{\color{green}{\left(-\frac{\pi}{3}\right)}}\right)\right)+{\color{purple}{(-2)}}\]
is in the form
\[\Large f(x) = {\color{red}{A}}\sin\left({\color{blue}{B}}\left(x-{\color{green}{C}}\right)\right)+{\color{purple}{D}}\]

So in this case,
\[\Large {\color{red}{A}} = {\color{red}{-7}}\]
\[\Large {\color{blue}{B}} = {\color{blue}{3}}\]
\[\Large {\color{green}{C}} = {\color{green}{-\frac{\pi}{3}}}\]
\[\Large {\color{purple}{D}} = {\color{purple}{-2}}\]

Answer 4

Let me know if that hint helps or not

Answer 5

ack! math! My hands itch. I can feel my tongue swelling. I gotta get outta here

Answer 6

this may help

https://i.ytimg.com/vi/ZMyeVkkGqyU/hqdefault.jpg

Answer 7

The person swapped C and D, but hopefully you can see how in my example C takes care of the horizontal shifting while D deals with the up and down shifting

Answer 8

@jim_thompson5910