The point (2,-16) is on the graph of f(x). Find the image of (2,-16) under each of the transformations.
1.y+d=f(x-c)
2. 1/3y= f(x-2)
3.y= |f(x-2)|
4. 2y= √|f(x)
5.y= 16/f(x)
What is the answer
To find the image of the point (2,-16) under each transformation, we need to replace x and y in the given equations with the corresponding values of the point (2,-16) and simplify.
1. y + d = f(x - c):
Replace x with 2 and y with -16:
-16 + d = f(2 - c)
The image of (2,-16) under this transformation depends on the value of d and c, as it shifts the graph vertically by d units and horizontally by c units.
2. (1/3)y = f(x - 2):
Replace x with 2 and y with -16:
(1/3)(-16) = f(2 - 2)
-16/3 = f(0)
The image of (2,-16) under this transformation is determined by the function f at x = 0 and setting y to -16/3.
3. y = |f(x - 2)|:
Replace x with 2 and y with -16:
-16 = |f(2 - 2)|
-16 = |f(0)|
The image of (2,-16) under this transformation depends on the function f at x = 0, and the absolute value ensures that the resulting image will have a positive y-value.
4. 2y = sqrt|f(x)|:
Replace x with 2 and y with -16:
2(-16) = sqrt|f(2)|
-32 = sqrt|f(2)|
The image of (2,-16) under this transformation is determined by the function f at x = 2, and the square root ensures that the resulting image will have a positive or negative y-value.
5. y = 16/f(x):
Replace x with 2 and y with -16:
-16 = 16/f(2)
The image of (2,-16) under this transformation depends on the function f at x = 2, and the reciprocal ensures that the resulting image will have a non-zero y-value.
Please note that in order to determine the exact image of the point (2,-16) under each transformation, you would need additional information about the function f and the specific values of d and c in the first transformation.