The graph of y = cos⁡ x is transformed to y = a cos ⁡(x − c) + d by a vertical compression by a factor of 1/2 and a translation 3 units up. the new equation is:

y = ½ cos (x + 3)

y = 2 cos x + 3

y = 2 cos x - 3

y = ½ cos x + 3

Last Option

Step-by-step explanation:

If the graph of the function  represents the transformations made to the graph of  then, by definition:

If   then the graph is compressed vertically by a factor k.

If   then the graph is stretched vertically by a factor k

If  then the graph is reflected on the x axis.

If the graph moves vertically upwards d units.

If the graph moves vertically down  d units.

In this problem we have the function

And we know that The graph of is transformed with  a vertical compression by a factor of 1/2 and a translation 3 units up

therefore it is true that and and  

Therefore the  new equation is:

the radius is 2 times the diameter.

step-by-step explanation: