ii. graph each function by finding the amplitude, period, phase shift, and vertical shift.\n9.) ( y = 2 cos…

ii. graph each function by finding the amplitude, period, phase shift, and vertical shift.\n9.) ( y = 2 cos x - 3 )\namp = ___ pd = ___\nshift = ___ v. shift = ___\n10.) ( y = sin ( x + pi ) + 4 )\namp = ___ pd = ___\np. shift = ___ v. shift = ___\n11.) ( y = \tan left( \frac { 1 } { 2 } x \right) + 1 )\namp = ___ pd = ___\np. shift = ___ v. shift = ___

ii. graph each function by finding the amplitude, period, phase shift, and vertical shift.\n9.) ( y = 2 cos x - 3 )\namp = ___ pd = ___\nshift = ___ v. shift = ___\n10.) ( y = sin ( x + pi ) + 4 )\namp = ___ pd = ___\np. shift = ___ v. shift = ___\n11.) ( y = \tan left( \frac { 1 } { 2 } x \right) + 1 )\namp = ___ pd = ___\np. shift = ___ v. shift = ___

Answer

Explanation:

Step1: Amplitude formula

For (y = A\cos(x)+k), amplitude is (|A|). For (y = 2\cos(x)-3), (A = 2), so amplitude (=|2| = 2).

Step2: Period formula

For (y = A\cos(Bx)+k), period is (\frac{2\pi}{|B|}). Here (B = 1), so period (=\frac{2\pi}{|1|}=2\pi).

Step3: Phase - shift formula

For (y = A\cos(B(x - C))+k), phase - shift is (C). For (y = 2\cos(x)-3) (equivalent to (y = 2\cos(1(x - 0))-3)), phase - shift (=0) (none).

Step4: Vertical - shift formula

For (y = A\cos(x)+k), vertical - shift is (k). Here (k=-3), so vertical - shift is down (3).

Answer:

Amplitude ( = 2), Period (=2\pi), Phase - shift (=\text{none}), Vertical - shift (=\text{down }3)