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

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 =

Horizontal shift =

Vertical shift = d

From the given sine function we can get the following values

a = 7

period =

horizontal shift = 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.

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1