 In a function, every input has a unique output, but in most cases, the relationship between input and output is too complicated to write. For example, the amount of time needed to complete a surgery is a function of the patient's health, the surgeon's skill, and the complexity of the operation, and the formula for the amount of time is... I don't have any idea. And this reflects a general rule of life. We are not so lucky that functions just fall out of the sky and hit us on the head. So, if we're very, very, very, very lucky, we'll get a function defined by a formula. And remember, no matter how awful the formula looks, it's better to have a formula than to not have a formula. And that means we'll have to learn how to work with them. So let's try to find the domain of f of x equals 8 minus 7x. So remember, the domain is a set of all possible input values. What can we put into this function? Well, let's think about it. The function requires us to take a value of x, then multiply it by 7, and subtract the result from 8. So what can we do that to? Well, certainly we can multiply any number by 7, and this will give us some number. But no matter what the product is, we can subtract the product from 8. And so the domain is all real numbers. Any real number can be input into this function. So we can write our domain in interval notation. x can be any number between minus infinity and positive infinity. How about a more complicated function? So again, let's think about what we do to an input value. Our input value is squared, multiplied by 3, and then these results are subtracted. So what can we do these operations to? We can do these operations to any real number. And so, since any real number can be squared, multiplied by 3, added, and subtracted, then our domain is all real numbers. More generally, this leads to the following results. Since any real number can be raised to a whole number of power, multiplied, added, or subtracted, that essentially describes any polynomial. And so we have the theorem, if f is a polynomial function, its domain is all real numbers. What about non-polynomial functions? So for example, let's take h of x be the absolute value of 13x minus 27 plus 7. So let's see what happens to our input value. Our input value x is multiplied by 13, then 27 is subtracted, after which we find the absolute value, and then we add 7. But the important thing to recognize here is we can do these things to any real number. And so the domain of h of x is all real numbers.