Final answer:
To get g(x), the translated function of f(x) = -3|x + 4| - 10, replace x with x - 7 and subtract 6 from the entire function, yielding g(x) = -3|x - 3| - 16.
Step-by-step explanation:
To find g(x), the translation 7 units right and 6 units down of f(x) = − 3|x + 4|−10, we need to adjust the function to account for these shifts. Translating a function to the right by d units requires replacing x with x − d. Therefore, to move f(x) right by 7 units, we replace every x with x − 7. Translating a function down by d units requires subtracting d from the entire function. Thus, to move f(x) down by 6 units, we subtract 6 from the entire function. The transformed function g(x) becomes:
g(x) = − 3|x − 7 + 4| − 10 − 6
g(x) = − 3|x − 3| − 16