9/20 - Sin/Cos Graphs and Phase Shift

What is the vertical shift for

 $y\ =\ -3\cos\left(4x\ +\pi\right)\ -\ 2$  ?

• up 2

• left 2

• right 2

• down 2

Tags

CCSS.HSF-IF.C.7E

Phase shift indicates ...

• An up or down movement

• A left or right movement

• A reflection over the y-axis

• A change in period

Tags

CCSS.HSF-IF.C.7E

What is the phase shift for the function

f(x) = -2sin(4x + π) - 1

• π

• -π

• -1

• -π⁄4

Tags

CCSS.HSF-IF.C.7E

What is the vertical shift for the function

f(x) = 4cos(2x + π) + 8

• right 8 units

• up 4 units

• down 8 units

• up 8 units

Tags

CCSS.HSF-IF.C.7E

Identify the phase shift of:

 $y=-3\cos\left(2x-\ \pi\right)+4$  

•  $\frac{\pi}{2}\$  to the left

•  $\pi\$  to the left

•  $\pi\$  to the right

•  $\frac{\pi}{2}\$  to the right

Tags

CCSS.HSF-IF.C.7E

Describe the shifts for the following graph without graphing.

 $y\ =\ 6\sin\left(3x\ +7\right)\ -\ 8$  ?

• shifted left and up

• shifted right and down

• shifted right and up

• shifted left and down

Tags

CCSS.HSF-IF.C.7E

Select the equation with the following criteria:
Reflection over x-axis
Amplitude = 6
Period = 2
Phase Shift left 1 unit
Vertical Shift up 5 units

•  $y=-6\cos\left(2x\ +\ 2\right)\ +5$  
  

•  $y\ =-6\sin\left(x+1\right)\ +\ 5$  

•  $y=-6\sin\left(2\pi x\ +\ 2\pi\right)\ +5$  
  

•  $y=-6\cos\left(\pi x+\pi\right)\ +\ 5$  

Tags

CCSS.HSF-IF.C.7E

Select the equation with the following criteria:

Amplitude = 2
Period = π/2
Phase Shift = π/4 to the right
Vertical Shift down 3 units

•  $y=2\sin\left(4x-\pi\right)-3$  
  

•  $y=-2\cos\left(2x-\frac{\pi}{2}\right)-3$  

•  $y=2\cos\left(x-\frac{\pi}{2}\right)-3$  
  

•  $y=2\sin\left(2x+\pi\right)-3$  

Tags

CCSS.HSF-IF.C.7E

Which equation does the graph represent?

•  $y=\sin\left(x+\frac{\pi}{4}\right)+2$  

•  $y=\cos\left(x-\frac{\pi}{4}\right)\ +2$  

•  $y=\cos\left(x-\pi\right)+2$  
  

•  $y=\sin\left(x+\frac{\pi}{2}\right)+2$  

Tags

CCSS.HSF-IF.C.7E

What is the equation for the following graph?

• $y=-0.5\sin\left(2x+\pi\right)$
  

• $y=0.5\cos\left(x-\frac{\pi}{2}\right)$

• $y=0.5\sin\left(3x-\frac{3\pi}{2}\right)$

• $y=-0.5\cos\left(x-\frac{\pi}{4}\right)$

Tags

CCSS.HSF-IF.C.7E