Question

URGENT URGENT HELP In what direction and by how many units is the graph of f(x) = 6 sin(2x + π) − 5 vertically and horizontally shifted?

Answer 1

Answer:

The required result is 5 unit vertically shifted downward and $\frac{\pi}{2}$ unit horizontally shifted left.

Step-by-step explanation:

Given : Graph $f(x) = 6\sin(2x+\pi)-5$

To find : In what direction and by how many units is the graph vertically and horizontally shifted?

Solution :

Vertically shift is up or down,

Vertically shifting down is shifting outside the function,

i.e, f(x)→f(x)-b

In the given graph, The graph is 5 unit vertically shifted downward as

$f(x) = 6\sin(2x+\pi)-5$ i.e, 5 unit shifted downward.

Horizontal shift is either left or right,

Horizontally shift left is shifting inside the function,

i.e,  f(x)→f(x+b)

We can write the given function as $f(x) = 6\sin(x+\frac{\pi}{2})-5$

In the given graph, The graph is $\frac{\pi}{2}$ unit horizontally shifted left as

$f(x) = 6\sin(x+\frac{\pi}{2})-5$ i.e, $\frac{\pi}{2}$ unit shifted left.

Therefore, The required result is 5 unit vertically shifted downward and $\frac{\pi}{2}$ unit horizontally shifted left.

Answer 2

A. Down 5, Left pi/2