Write the equation of the transformed graph of sine with period that has been shifted horizontally to the right 5 units, has an amplitude of 3, and has been flipped across the x-axis. (3 points)

Question

 Write the equation of the transformed graph of sine with period that has been shifted horizontally to the right 5 units, has an amplitude of 3, and has been flipped across the x-axis. (3 points)

Answer 1

The general equation for the transformed graph is

y = ±a sin (bx – c)

You need to figure out

1. a and where it's positive or negative. The magnitude of a = amplitude
2. b which is related to the period
3. c which is related to the horizontal shift (also called phase shift)

a = amplitude = 3

flipped across the x-axis means start with –a = –3

period = π = 2π/b, so b = 2π/(period) = 2π/ π = 2

phase shift (horizontal shift to the right) = 5 = c/b, so c = 5b = 5 × 2 = 10

So our required equation is

y = –3 sin (2x – 10)

Answer 2

f(x) = -3sin(2(x-5))

The negative sign in front of the sine function results in an x-axis reflection.

The 3 in front of the sine function results in an amplitude of 3, which is 3 tImes the sine wave's normal amplitude of 1. This is peak amplitude which is measured from wave midline to either peak. Peak-to-peak amplitude is measured from a wave trough to a wave peak; its value is twice peak amplitude.

The period of a sine wave is normally 2π. To change this period to half of that (π), we need to double the frequency. We do that by changing x to 2x.

A shift of 5 units is accomplished by subtracting 5 units from x inside the parentheses. Subtracting inside the parentheses moves the wave right; adding moves the wave left. Inside the parentheses, parameters work opposite to the way most people intuitively think.

https://www.desmos.com/calculator/ipvb0okeom