Question

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

Down 2, right pi over 3
Down 2, left pi over 3
Up 2, right pi over 3
Up 2, left pi over 3

Answer 1

Option 1. Down 2, right pi over 3.

Explanation:

In a given function f(x) = -7 sin(3x+π)-2 we have to find the shift horizontally and vertically.

As we know in a sine equation represented as y = a sin(bx+c) +d

Amplitude of the wave = a

Period =
`(2\pi )/(b)`

Horizontal shift =
`(\pi )/(b)`

Vertical shift = d

From the given sine function we can get the following values

a = 7

period =
`(2\pi )/(3)`

horizontal shift =
`(\pi )/(3)` in the right side since it's with positive sign.

Vertical shift = -2 down with 2 ( since it's with negative sign)

Therefore Option 1 is the correct one.