Question

The graph of y=cos ⁡x is transformed to y=a cos⁡(x−c)+d by a vertical expansion by a factor of 3, then translated π/2 units left and 2 units up. The new equation is:

y = 3 cos (x + π/2) + 2

y = 1/3 cos (x - π/2) + 2

y = 3 cos (x - π/2) - 2

y = 3 cos (x - π/2) + 2

Answer 1

y = 3 cos (x + π/2) + 2

Explanation:

The transformed equation of y = Cos x is y=a cos⁡(x−c)+d

Where

• a is the amplitude. (if a > 1 we have vertical stretch/compression of factor a)

• if function is translated c units left, it will be +c and if c units right, it will be -c

• d is the vertical shift. If +d, then it is translated d units up and if -d, it is translated d units down

Keeping these points in mind, the correct equation should have a = 3, c = + π/2, and d = +2

So we can write:

y = 3 cos (x + π/2) + 2

first answer choice is right.