14I&J Horizontal/vertical translations of sin and cos graphs

What is the equation of the graph?

• y = - 6 cos x - 1
• y = 3 cos x - 4
• y = -7 cos x 
• y = -3 cos x - 4 

Which equation best represents the graph pictured above?

• $y=3\sin x+1$

• $y=3\cos x+1$

• $y=2\sin x+1$

• $y=2\cos x+1$

What is the vertical translation for

y = 4 cos(x +π) - 2?

• up 2

• left 2

• right 2

• down 2

Which is a correct equation for the graph shown?

• $y=-4\sin x+2$

• $y=-4\cos x+2$

• $y=-4\sin\left(x+2\right)$

• $y=4\sin\left(x\right)+2$

Which is a correct equation for the graph shown?

• $y=\frac{1}{2}\cos\left(2x\right)-3$

• $y=\frac{1}{2}\cos\left(\frac{1}{2}x\right)-3$

• $y=\frac{1}{2}\cos\left(2x+3\right)$

• $y=\frac{1}{2}\sin\left(2x\right)-3$

The graph shown has equation:

• $y=5\sin\left(πx\right)$

• $y=3\sin\left(2x\right)+2$

• $y=\sin\left(x\right)+2$

• $y=3\sin\left(πx\right)+2$

A horizontal translation can also be known as a

(a)  

The graph of the following function $y=\sin\ \left(x-\frac{\pi}{2}\right)$  is: 

• translated  $\frac{\pi}{2}$  units in positive direction of the x-axis

• translated  $\frac{\pi}{2}$  units in negative direction of the x-axis

• translated  $\frac{\pi}{2}$  units in positive direction of the y-axis

• translated  $\frac{\pi}{2}$  units in negative direction of the y-axis

For the function f: [0, 2 $\pi$  ]  $\rightarrow$  R,  $y=\cos\ \theta\ -1$  . 

The x-intercepts are:

• (0,1) and (2 $\pi$  , 1)

• (0,0) and (2 $\pi$  , 0)

• ( $\left(\frac{\pi}{2},\ 0\right)\ and\ \left(\frac{3\pi}{2},0\right)$  

• (1, 0) and $\left(2\pi,\ 0\right)$  

For the function $y=\cos\ \left(3x\ +\pi\right)-1$  . The vertical translation is 

(a)