Question

the point (5,9) is on the function y=f(x).State the mapping rule and the corresponding coordinates 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 transformed function g(x) = -2f(0.75(x-5))-6 is as follows:

1. Take the x-coordinate of the original point (5) and subtract 5 from it → 5-5 = 0.
2. Multiply the result from step 1 by 0.75 → 0 * 0.75 = 0.
3. Subtract the result from step 2 from 0 → 0 - 0 = 0.
4. Take the result from step 3 and plug it into the original function f(x) → f(0) = 9.
5. Multiply the result from step 4 by -2 → 9 * -2 = -18.
6. Subtract 6 from the result in step 5 → -18 - 6 = -24.

Therefore, for the point (5,9) on the original function y = f(x), the corresponding coordinates on the transformed function g(x) = -2f(0.75(x-5))-6 is (5,-24).