Answer:
For a function f(x) = y.
The independent variable is the one that we chose to input in the function, in this case, is x, and the dependent variable is the variable that changes in response to the independent variable, in this case, is y.
In this problem we have:
"Sammy has $180 in her savings account and plans to deposit $20 each month."
We can define:
y = money in her savings account
x = number of months that have been passed since she started saving.
Originally, she has $180, and she saves $20 per month, so if x months have been passed, the total amount of money in her savings account is:
y = f(x) = $180 + $20*x
Now we want to know if this function is continuous or discrete, to see this we need to look at the possible values of x.
x represents the number of months that have been passed, then the values that x can take are:
x = 0, 1, 2, 3, 4, ...
So x can only take the values of positive integers, this means that the domain of x is discrete, then the function f(x) is a discrete function.
