Final answer:
To make the function f(x) = (x + 6)^4 - 6 one-to-one, we must restrict its domain so there's only one x-value for every y-value. One way to restrict it is by setting the domain to x ≥ -6 which only includes the increasing portion of the function.
Step-by-step explanation:
To make the function f(x) = (x + 6)^4 - 6 one-to-one, we must restrict the domain so that the function passes the horizontal line test.
In its current form, for every y-value on the graph, there could be more than one x-value due to the nature of the fourth power function (it's even and symmetric).
Therefore, to make f(x) one-to-one, we need to limit the domain to either non-negative or non-positive x values.
For instance, if we choose to restrict the domain to x ≥ -6, this means we are considering x values where x + 6 is greater than or equal to zero.
This restricted domain will give us only the increasing portion of the function, making f(x) one-to-one.