What Is A Function | Algebra | Maths | FuseSchool
A function is an operation, or series of operations, that transforms a set of numbers into a different set. We put our input into the function, operations are performed on it, and a different number is outputted. If we have this function f(x) = 5x - 2, x stands for the input and what f(x) equals is the function. So 5x - 2 is the function here. f(x) is the mathematical notation. Think of it in a similar way to how you think of y. We say “a function of x” equals 5x - 2. If we wanted to calculate the value of f(3) we just need to replace x in the function with 3. f(3) = 5 (3) - 2 = 15 - 2 = 13. f(3) = 13. If f(x) = x-squared - 2x, then f(4) = 4X4 - 2X4, so f(4) = 8. If f(x) = 15 - 4x, calculate the value of x when f(x) = 35. This time we’re not being asked to substitute in a value of x, but instead are being told the function equals 35. So the output is 35. It wants us to find x (the input). We just need to solve 15 - 4x = 35. So x = -5. So an input of -5 will give an output of 35. For functions, you will usually see the letter F, but it can be anything. You’ll see g(x) h(x) and many other letters. They all mean the same thing:“a function of x” equals... There are two special rules which determine whether something is a function or not. The function must work for every input value. Every input value can only give one output value. Different inputs can share the same output, but each input can only give the one output. The final piece of the functions puzzle that we need to address in this introductory video are the words domain and range. We will come across these a lot when learning about functions. The domain just means the inputs. The domain can be a range of values, or just one value. The range are the output values from the function - so what comes out when we put our domain values in. We’ll look at composite functions, inverse functions and the graphs of functions in other videos.
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