Final answer:
The equation 69 = 38 - 9 is a constant and does not have a variable; however, if q is to be considered as the independent variable, the simplest function notation would be f(q) = 69, stating the function value remains 69 regardless of q.
Step-by-step explanation:
To write the equation in function notation, we need to express the equation as a function of an independent variable named q. In the equation given 69 = 38 - 9, there is no variable present, meaning it's a constant value. As we're asked to treat 'q' as the independent variable, we can arbitrarily decide that 'q' could equal any value, because it is not present in the original equation. An example of introducing the variable q would be by writing the constant equation as a function, the simplest representation of which could be f(q) = 69. This indicates that no matter the value of q, the function f will always yield a result of 69.
An example from algebra that shows the utility of function notation might be expressing a linear equation like 7y = 6x + 8. The independent variable here is x, and if we were to convert this into function notation, it would become f(x) = (6/7)x + 8/7. This shows how function notation can clearly indicate the relationship between variables.