How do you find the amplitude, period, and shift for #f(x) = −4 sin(2x + π) − 5#?
First, let us make this equation in a different format
Only the inside of the sin must change.
We get this to be
Now we have
The amplitude is always the absolute value of the coefficient of sin
This means that the amplitude is
The period can be denoted as
So we have
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.
and vice versa
Can you find the horizontal shift after knowing this?
It is a shift to the LEFT by