Question

Write an equation that models each of the following translations

Answer 1

The equation will be y = -1 + 2 sin ( 2x - 1 )

Explanation:

See the attached image

Answer 2

`y = - 1+ 2 \sin(2x - 1)`

EXPLANATION

The given equation is

`y = 1 + 2 \sin(2x - 1)`

This function is of the form,

`y = a \sin(bx - c) + d`

The value of d=1 shifts the graph up by one unit.

If we want to shift the graph, 2 units down, then, we have to add -2 to d=1.

The transformed equation is,

`y = - 2 + 1 + 2 \sin(2x - 1)`

which gives us,

`y = - 1+ 2 \sin(2x - 1)`