directions: for 6 - 8, graph the following functions.\n6. graph ( y = 3 cos left( \frac { 1 } { 2 } x…

directions: for 6 - 8, graph the following functions.\n6. graph ( y = 3 cos left( \frac { 1 } { 2 } x \right) - 1 )\namplitude: \nmidline: \nperiod: \nphase shift: \n7. graph ( y = - 2 sin 2 left( x + \frac { pi } { 4 } \right) )\namplitude: \nmidline: \nperiod: \nphase shift: \n8. graph ( y = 2 - 3 cos pi ( x ) )\namplitude:
Answer
Explanation:
Step1: Midline for (y = -2\sin2(x+\frac{\pi}{4}))
For a function of the form (y = A\sin(B(x - C))+D), the midline is (y = D). Here (A=-2), (B = 2), (C=-\frac{\pi}{4}), (D = 0). So the midline is (y = 0).
Step2: Period for (y=-2\sin2(x+\frac{\pi}{4}))
The formula for the period of (y = A\sin(B(x - C))+D) is (T=\frac{2\pi}{|B|}). Given (B = 2), then (T=\frac{2\pi}{2}=\pi).
Answer:
Midline: (0), Period: (\pi)