Then you can figure out which is the independent variable and which is the dependent variable: (Independent variable) causes a change in (Dependent Variable) and it isn't possible that (Dependent Variable) could cause a change in (Independent Variable). For example: (Time Spent Studying) causes a change in (Test Score) and it isn't possible that (Test Score) could cause a change in (Time Spent Studying).
Domain and Range. When we look at a function like f(x) = x + 2, we can easily say where the function f(x), in this case, the value along the y-axis, is at any point we choose along the x-axis. We know that at x = 3.4, f(x) = 5.4. The values of x that the function will output a value for is called the domain of f. In the case of f(x) = x + 2, the domain is the entire x-axis, or, formally speaking, all real numbers. The values which f(x) takes on is called the range of f.
To understand domain and range of rational functions, we take an example of rational function f(t). Let f(t) = $\frac{t + 3}{t^2 - 5t - 66}$. Now, to find the domain, we first factor the denominator of the function f (t). The denominator of function f(t) is t2 - 5t - 66. To factor this, we divide -5t, such that addition becomes -5t and multiplication becomes -66. So, the term t2 - 5t - 66 contains two factors (t - 11) and (t + 5).