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

1 Answer
Anthony X
Feb 12, 2016

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#

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