Question

the point (5,9) is on the fuction y=f(x). state the mapping rule and the corresponding coorddinates of the point for the transformed function g(x)=-2f(0.75(x-5))-6

Answer 1

[AI-generated answer — Bot GPT 3.5]

The mapping rule for the transformation of the function g(x) = -2f(0.75(x-5))-6 is:

1. Multiply the input (x-coordinate) by 0.75.
2. Subtract 5 from the result of step 1.
3. Apply the function f(x) to the result of step 2.
4. Multiply the output (y-coordinate) of step 3 by -2.
5. Finally, subtract 6 from the result of step 4.

To find the corresponding coordinates of the point (5,9) in the transformed function g(x), we follow these steps:
1. Multiply the x-coordinate by 0.75: 5 × 0.75 = 3.75.
2. Subtract 5 from the result of step 1: 3.75 - 5 = -1.25.
3. Apply the function f(x) to the result of step 2: f(-1.25) = ??? (unknown without the function f).
4. Multiply the output of step 3 by -2: ??? × -2 = ??? (unknown until f(-1.25) is known).
5. Finally, subtract 6 from the result of step 4: ??? - 6 = ??? (unknown until the value in step 4 is known).

Without knowing the function f(x) or the value f(-1.25), we cannot determine the corresponding coordinates of the point (5,9) in the transformed function g(x)=-2f(0.75(x-5))-6.