Question

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

Down 5, left pi over 2
Up 5, left pi over 2
Down 5, right pi over 2
Up 5, right pi over 2

Answer 1

(D) The direction is Up 5, right pi over 2!

goodluck! :-)

Answer 2

Option 1 is correct.

Explanation:

Given graph of f(x)=6 sin(2x + π) - 5

we have to tell in what direction the graph vertically and horizontally shifted.

As, f(x+1) is a change on the inside of function, giving a horizontal shift left by 1, and the subtraction by 3 in f(x+1)-3 is a change to the outside of function, giving a vertical shift down by 3.

Hence, the graph of f(x)=6sin(2x + π) - 5

Here, change on the inside of function, giving a horizontal shift left by
`(\pi)/(2)`, and subtraction by 5 in function is a change to the outside of function, giving a vertical shift down by 5.

Option 1 is correct.