Answer: Last Option
[tex]Y =\frac{1}{2}cosx + 3[/tex]
Step-by-step explanation:
If the graph of the function [tex]y=kf(x) +d[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <k <1[/tex] then the graph is compressed vertically by a factor k.
If [tex]|k| > 1[/tex] then the graph is stretched vertically by a factor k
If [tex]k <0[/tex] then the graph is reflected on the x axis.
If [tex]d> 0[/tex] the graph moves vertically upwards d units.
If [tex]d <0[/tex] the graph moves vertically down d units.
In this problem we have the function [tex]y = cosx[/tex]
And we know that The graph of [tex]y = cosx[/tex] is transformed with a vertical compression by a factor of 1/2 and a translation 3 units up
therefore it is true that [tex]0 <k <1[/tex] and [tex]k=\frac{1}{2}[/tex] and [tex]d =3> 0[/tex]
Therefore the new equation is:
[tex]Y =\frac{1}{2}cosx + 3[/tex]
