Final answer:
To translate the function f(x) = x² + 5 upward by 5 units and to the right by 1 unit, you need to adjust the variables accordingly. The translated function is f(x) = (x - 1)² + 10.
Step-by-step explanation:
To translate a function upward by 5 units and to the right by 1 unit, you need to adjust the variables accordingly. In this case, the function f(x) = x² + 5 would become f(x) = (x - 1)² + 10.
By subtracting 1 from the variable x, the function is shifted 1 unit to the right. Then, by squaring the new variable (x - 1), the function is adjusted to account for the upward translation of 5 units. Finally, adding 10 to the original function accounts for both translations.
The translated function is f(x) = (x - 1)² + 10.