Need help figuring this problem out.
The following points are on the graph of: y=f(x)
(-5,0),(-2,2),(0,0),(2,-4) and (4,0)
Use theorem to identify the corresponding points on the transformed functions.
y = 2f(x-3)-2
To find the corresponding points on the transformed function y = 2f(x-3) - 2, we need to apply the given transformations step by step to the original points.
Let's start with the original points:
(-5, 0), (-2, 2), (0, 0), (2, -4), and (4, 0).
1. Translation:
The transformation (x-3) in the equation represents a horizontal translation to the right by 3 units. To apply this transformation, we need to subtract 3 from the x-coordinate of each point.
The translated points are:
(-5 - 3, 0), (-2 - 3, 2), (0 - 3, 0), (2 - 3, -4), and (4 - 3, 0).
This simplifies to:
(-8, 0), (-5, 2), (-3, 0), (-1, -4), and (1, 0).
2. Amplification:
The transformation 2f(x) represents a vertical stretch, where every y-coordinate in the original function is multiplied by 2. Let's multiply the y-coordinate of each translated point by 2.
The amplified points are:
(-8, 0), (-5, 4), (-3, 0), (-1, -8), and (1, 0).
3. Vertical Shift:
Finally, the transformation -2 in the equation represents a vertical shift downward by 2 units. To apply this transformation, we need to subtract 2 from the y-coordinate of each amplified point.
The final transformed points are:
(-8, 0 - 2), (-5, 4 - 2), (-3, 0 - 2), (-1, -8 - 2), and (1, 0 - 2).
This simplifies to:
(-8, -2), (-5, 2), (-3, -2), (-1, -10), and (1, -2).
Therefore, the corresponding points on the transformed function y = 2f(x-3) - 2 are:
(-8, -2), (-5, 2), (-3, -2), (-1, -10), and (1, -2).