Final answer:
To translate the function f(x) = -9x + 10 one unit to the left, we replace x with (x + 1) and simplify to get g(x) = -9x + 1. This new function g(x) represents the original function shifted to the left on the x-axis by one unit.
Step-by-step explanation:
To find the function g(x), which is a translation of f(x) = -9x + 10 one unit to the left, we apply a basic transformation rule. The rule states that for any function f(x), the function f(x + d) is f(x) translated d units to the left on the x-axis. Since we are translating the function one unit to the left, we substitute x with x + 1 in the original function.
Therefore, g(x) = f(x + 1) becomes g(x) = -9(x + 1) + 10. Simplifying this results in:
g(x) = -9x - 9 + 10
g(x) = -9x + 1.
So, g(x) is the function -9x + 1, which is the given function f(x) translated 1 unit to the left.