Identify all of the transformations for the function f(x) = 3cos(−x + π/3)−2 . Check all that apply(4 points) Responses vertical shift down 2 units vertical shift down 2 units reflection over the x-axis reflection over the x-axis horizontal shift to the right π3 horizontal shift to the right pi over 3 vertical shift up 2 units vertical shift up 2 units horizontal shift to the left π3 horizontal shift to the left pi over 3 Vertical stretch by 3 Vertical stretch by 3 reflection over the y-axis reflection over the y-axis
The transformations for the function f(x) = 3cos(−x + π/3)−2 are:
1) Vertical shift down 2 units: This is because there is a -2 added to the function, which shifts the graph down by 2 units.
2) Reflection over the x-axis: The negative sign before the x in -x reflects the graph over the x-axis.
3) Horizontal shift to the right π/3: The π/3 added inside the cosine function shifts the graph horizontally to the right by π/3 units.
4) Vertical stretch by 3: The coefficient of 3 in front of the cosine function stretches the graph vertically by a factor of 3.
Therefore, the correct answers are:
- Vertical shift down 2 units
- Reflection over the x-axis
- Horizontal shift to the right π/3
- Vertical stretch by 3