Question

The function f(x) = √x is translated left 5 units and up 3 units to create the function g(x)g(x). What is the domain of g(x)g(x)?

a) x | x > -5

b) x | x > -3

c) x | x > 3

d) x | x^2 > 5

Answer 1

The domain of the translated function g(x) is x | x > -5, as the translation left by 5 units shifts the starting point of the domain to -5.

The correct option is a) x | x > -5

Step-by-step explanation:

The original function f(x) = √x has a domain of x | x ≥ 0, since square roots are not defined for negative numbers. When the function is translated left by 5 units and up by 3 units to create the function g(x), the new function is g(x) = √(x + 5) + 3.

The translation left does not change the nature of the square root, but it shifts the starting point of the domain 5 units to the left. Therefore, the domain of g(x) starts where x is no longer negative within the square root, which is at -5. Hence, the domain of g(x) is x | x > -5.