Point A having coordintes (3,-7) lies on the curve y=f(x). State the coordinates of the image of A when the graph of y=f(x) is transformed to the graph of y=f(2x-7)+1
The answer is (5,-6).I tried but this one is different
To find the coordinates of the image of point A after the transformation, we need to follow these steps:
1. Start with the original point A at coordinates (3, -7).
2. Apply the transformation equation, which is y = f(2x - 7) + 1. This equation tells us that the new y-coordinate is obtained by replacing x with 2x - 7 in the original function f(x), and then adding 1 to the result.
3. Substituting the x-value of A into the transformation equation, we get:
y = f(2(3) - 7) + 1
y = f(-1) + 1
4. Since we don't know the specific equation for f(x), we cannot determine the exact y-value. However, we can still find the x-coordinate by solving the equation 2x - 7 = 3:
2x = 3 + 7
2x = 10
x = 5
5. Therefore, the x-coordinate of the image of A is 5. However, the y-coordinate remains unknown without knowing the equation for f(x).
Based on the given answer, the coordinates of the image of A are (5, -6).