Question

Which statement is correct regarding g(x) = 35x + 6 - 8 and the parent function f(x) = x ?

O The domains of g(x) and f(x) are the same, but their ranges are not the same.

O The ranges of g(x) and f(x) are the same, but their domains are not the same.

The ranges of g(x) and f(x) are the same, and their domains are also the same.

O The domains of g(x) and f(x) are the not the same, and their ranges are also not the same.

Answer 1

The ranges of g(x) and f(x) are the same and their domains are also the same.

Explanation:

The function g(x) is the function f(x) multiplied by 35 and later translated twice, first 6 units up and later 8 units down. Since, both expressions are linear functions, both are continuous and both have the same domains and range due to constant slope.

Hence, the ranges of g(x) and f(x) are the same and their domains are also the same.