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- A function is generally denoted by f (x) where x is the input. The general representation of a function is y = f (x).
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For essence 'h (a) = x*a + b', where 'x' is the slope of the function and 'b' is the Y-axis intersection, or what you call is as a "Y intersect". ( Remember 'b' can either be positive or negative) A function is nothing but a number "operator" it takes some numbers & variables, fiddles with it and gives only one output.
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- Functions
A function is like a machine that takes an input and gives...
- 4 Years Ago Posted 4 Years Ago. Direct Link to Toska Pi's Post “Hi! I Was Wondering If Th
- Input, Relationship, Output
- Some Examples of Functions
- Names
- The "X" Is Just A Place-Holder!
- Sometimes There Is No Function Name
- Relating
- What Types of Things Do Functions Process?
- A Function Is Special
- The Two Important Things!
- Vertical Line Test
We will see many ways to think about functions, but there are always three main parts: 1. The input 2. The relationship 3. The output
But we are not going to look at specific functions ... ... instead we will look at the general ideaof a function.
First, it is useful to give a function a name. The most common name is "f", but we can have other names like "g" ... or even "marmalade" if we want. But let's use "f": We say "f of x equals x squared" what goes intothe function is put inside parentheses () after the name of the function: So f(x) shows us the function is called "f", and "x" goes in ...
Don't get too concerned about "x", it is just there to show us where the input goes and what happens to it. It could be anything!
Sometimes a function has no name, and we see something like: y = x2 But there is still: 1. an input (x) 2. a relationship (squaring) 3. and an output (y)
At the top we said that a function was likea machine. But a function doesn't really have belts or cogs or any moving parts - and it doesn't actually destroy what we put into it! A function relatesan input to an output. Saying "f(4) = 16" is like saying 4 is somehow related to 16. Or 4 → 16
So we need something more powerful, and that is where setscome in: Each individual thing in the set (such as "4" or "hat") is called a member, or element. So, a function takes elements of a set, and gives back elements of a set.
But a function has special rules: 1. It must work for everypossible input value 2. And it has only one relationshipfor each input value This can be said in one definition:
When a relationship does not follow those two rules then it is not a function ... it is still a relationship, just not a function.
On a graph, the idea of single valuedmeans that no vertical line ever crosses more than one value. If it crosses more than once it is still a valid curve, but is not a function. Some types of functions have stricter rules, to find out more you can read Injective, Surjective and Bijective
Jun 14, 2024 · In this section we will formally define relations and functions. We also give a “working definition” of a function to help understand just what a function is. We introduce function notation and work several examples illustrating how it works. We also define the domain and range of a function.
A specific element x of X is a value of the variable, and the corresponding element of Y is the value of the function at x, or the image of x under the function. A function f, its domain X, and its codomain Y are often specified by the notation :.
Aug 24, 2022 · To use a graph to determine the values of a function, the main thing to keep in mind is that \(f(input) = ouput\) is the same thing as \(f(x) = y\), which means that we can use the \(y\) value that corresponds to a given \(x\) value on a graph to determine what the function is equal to there.
A function is like a machine that takes an input and gives an output. Let's explore how we can graph, analyze, and create different types of functions.
X and Y Graph is a graph that showcases both the x-axis and y-axis that form the coordinate planes for a graph. Learn more about the interesting concept of x and y graph, its definition, equations along with solving a few examples.
