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

Please someone help me. Thank you.

Answer 1

I think its down 2 left pi/3, but did you get the answer?

Answer 2

Down 2, left pi over 3

Explanation:

f(x) = −7 sin(3x + π) − 2

Given equation is in the form of

f(x) = A sin(Bx+C) + D

Horizontal shift left is C/B and right is -C/B

Vertical shift up is +D and down is -D

From the given equation C=
`\pi`

B= 3

So C/B is
`(\pi )/(3)`

C/B is positive so graph will move left by pi/3

We know d is -2

So graph will move down by 2 units