Identify the transformations needed to graph the cosine function y = –0.5cos(x) – 3 from the parent cosine function. check all that apply.
vertical compression by a factor of 0.5
reflection across the y-axis
vertical translation 3 units down
vertical stretch by a factor of 0.5
reflection across the x-axis
vertical translation 3 units up
vertical translation 0.5 units down

Vertical translation 3 units down, vertical compression by a factor of 0.5, and reflection across the x-axis. This is because since the number -3 is outside of the parenthesis, it is a vertical translation and is since it is negative it is 3 down. If the number multiplied by the function is less than 1 it is a compression and if it is greater than 1 it is a stretch. And the negative represents the reflection across the x axis.