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

Answer:

Option 1. Down 2, right pi over 3.

Step-by-step 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 = $\frac{2\pi }{b}$

Horizontal shift = $\frac{\pi }{b}$

Vertical shift = d

From the given sine function we can get the following values

a = 7

period = $\frac{2\pi }{3}$

horizontal shift = $\frac{\pi }{3}$ 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.