Question

Which equation represents the resulting function after translating f(x) = x three units in the negative y-direction and eight units in the negative x-direction?

a) ( f(x) = 1/2x + 8 - 3 )
b) ( f(x) = √5 - 8 - 3 )
c) ( f(x) = √x+3 - 8 )
d) ( f(x) = √3 - 3 + 8 )

Answer 1

The translated function after moving three units down and eight units to the left is f(x) = x + 5. None of the provided options match this result, leading to the conclusion that there might be an error in the question or that more information is needed.

Step-by-step explanation:

To find the equation representing the function after the given translations, we must adjust the original function, f(x) = x, accordingly. Translating a function three units in the negative y-direction equates to subtracting 3 from the function. Therefore, the term -3 will be added to the equation. Translating eight units in the negative x-direction means we will be adding 8 to the x-value before applying the function, thus the function becomes f(x + 8). The original function is a linear function represented by f(x) = x; after the translations, it will become f(x) = (x + 8) - 3. Simplifying this we have f(x) = x + 5. From the provided options, none explicitly matches this final translated function, suggesting a possible error in the options or the need for clarification from the student.