Function notation what is

This is a special notation used only for functions. However, f x is not the only variable used in function notation. You can use any letters, but they must be in the same format - a variable followed by another variable in parentheses.

Often times functions are written as an abbreviation. For example, if you are writing an equation to calculate the square of x. You may write this as a function and name it s x. This is read as "s of x" for the "square of x". Another example would be if I were writing an equation to determine the distance a car travels based on a certain time driving.

I may write the function as d t for "the distance based on the time". This way, I know that t, which represents "time" is my independent variable and d t is the outcome. Remember when we graphed linear equations? This is what is known as function notation. This is NOT the multiplication of f times x. Names have different letters, such as f x and g x. The graphing calculator does distinctive function naming with Y1, Y2, Equivalent Notations!

To evaluate a function, substitute the input the given number or expression for the function's variable place holder, x. Replace the x with the number or expression. Solution: Substitute 4 into the function in place of x. This answer can be thought of as the ordered pair 4,7. The answer may also be referred to as the image of 4 under f x. Solution: Substitute -3 into the function in place of b. That's why we call Y the dependent variable.

So one way this is written is it's kind of different from what you've seen before. What you've seen before is probably something like this.

Y equals 3X plus 2. A new way to write that is using what's called function notation. Instead of Y, I'm going to say F of X. What that means is the function that's using X is equal to 3X plus 2. It's the same thing written in two different ways. I think it's kind of neat when we get into doing some more problems with numbers is that I can stick a number in there for X and I can show what number that is here as well. You can kind of tell what X number you're plugging in, the independent variable, to get your Y value output variable.

One last thing to keep in mind when you're working with functions and function notation is the ideas of domain and range. Domain is the set of all X values or the independent variables.

Range is the set of Y values or the dependent variables. Which means that your domain changes on its own.