Question

How do you find the amplitude, period, and shift for `f(x) = −4 sin(2x + π) − 5`?

Answer 1

First, let us make this equation in a different format
`f(x) = A sin( B ( x + C)) + D`

Only the inside of the sin must change.
We get this to be `2(x + pi/2)`

Now we have `f(x) = -4 sin( 2(x + pi/2)) -5`

The amplitude is always the absolute value of the coefficient of sin

This means that the amplitude is `4`

The period can be denoted as `(2pi)/b` where b is the coefficient inside the sin

So we have `2pi/2` ===> `pi`

Now the vertical shift is easy: it is just the D value, which is a vertical shift down by 5 units

The horizontal shift is somewhat tricky. It is related to the C value
Similar to radical functions, this horizontal shift is the opposite of the sign.

For example: `(x - pi)` would be a horizontal shift to the RIGHT by `pi`

and vice versa

Can you find the horizontal shift after knowing this?

It is a shift to the LEFT by `pi/2`