The graph of y(x) is transformed to give the graph of y=-f(x+3).
The point A on the graph of y=f(x) is mapped to the point P on the graph of y= -f(x+3)
The coordinates of point A are (9,1)
Find the coordinates of point P.
f(9) = 1
-f(6+3) = -1
(9,1) becomes (6,-1)
Well, let's start by understanding the transformation of the graph. When we have y = -f(x+3), the transformation involves a reflection across the x-axis and a horizontal shift to the left by 3 units.
Now, if the original point A(9,1) is mapped to point P on the transformed graph, we can apply the transformation to find the coordinates of P.
First, let's apply the horizontal shift to point A. Moving 3 units to the left, we get A'(-6,1).
Next, let's apply the reflection across the x-axis. Flipping the y-coordinate, we get A'(-6,-1).
So, the coordinates of point P on the transformed graph are (-6,-1). Voilà!
To find the coordinates of point P, we need to apply the given transformation to point A.
The transformation involves taking the opposite of the y-coordinate and shifting the x-coordinate to the left by 3 units.
Since point A has coordinates (9,1), we can apply these transformations step by step:
1. Opposite of the y-coordinate:
The y-coordinate of point A is 1. Taking the opposite gives -1.
2. Shifting the x-coordinate to the left by 3 units:
The x-coordinate of point A is 9. Shifting it to the left by 3 units gives 9 - 3 = 6.
Therefore, the coordinates of point P are (6, -1).
To find the coordinates of point P on the graph of y = -f(x+3), which is the transformation of the graph of y = f(x), we can use the given information and apply the necessary transformations.
1. Start with the coordinates of point A: (9, 1).
2. The transformation y = -f(x+3) involves two main transformations:
a. A reflection in the x-axis (y = -f(x)), which changes the sign of the y-coordinate.
b. A horizontal shift to the left by 3 units (y = -f(x+3)), which affects the x-coordinate.
3. Apply the reflection in the x-axis by changing the sign of the y-coordinate of point A: (9, -1).
4. Apply the horizontal shift to the left by 3 units by subtracting 3 from the x-coordinate of point A: (9 - 3, -1) = (6, -1).
Therefore, the coordinates of point P on the graph of y = -f(x+3) are (6, -1).