The graph of y = f(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 co-ordinates of point A are (9,1).
Find the co-ordinates of point P.
Thank you very much
What is 12,-1
To find the coordinates of point P on the graph of y = -f(x+3), we need to apply the given transformation to the coordinates of point A.
Let's first analyze the transformation y = -f(x+3):
- The negative sign in front of f(x+3) indicates a reflection of the original graph across the x-axis.
- The term (x+3) inside f(x+3) implies a horizontal shift of 3 units to the left (opposite direction from the positive sign).
Given point A with coordinates (9, 1), we can apply the transformation step-by-step:
1. Reflection across the x-axis: The y-coordinate of point A changes its sign and becomes -1.
Point A' = (9, -1)
2. Horizontal shift 3 units to the left: The x-coordinate of point A' is decreased by 3.
Point P = (9 - 3, -1) = (6, -1)
Therefore, the coordinates of point P on the graph of y = -f(x+3) are (6, -1).
To find the coordinates of point P on the graph of y = -f(x+3) given the coordinates of point A as (9,1), we need to understand how the transformation affects the original graph.
The given transformation is y = -f(x+3), which means we are taking the opposite of the function value (-f(x)) and shifting the graph horizontally to the left by 3 units (x+3). Let's analyze the transformation step by step:
1. Taking the opposite: The original function f(x) is multiplied by -1, so the positive y-values become negative and vice versa. This reflects the graph across the x-axis.
2. Shifting left by 3 units: The original x-values are now replaced with (x+3), which means the entire graph is shifted to the left by 3 units.
Now, let's apply these transformations to find the coordinates of point P:
1. Opposite of the y-coordinate: Start with the y-coordinate of point A, which is 1, and take the opposite of it. So, -1.
2. Shifting left by 3 units: Take the x-coordinate of point A, which is 9, and subtract 3 to shift it to the left. So, 9-3 = 6.
Therefore, the coordinates of point P on the graph of y = -f(x+3) are (6, -1).