What is a function? | Functions and their graphs | Algebra II | Khan Academy

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Function, let’s try to understand it In an abstract way, It converts a specific input Adjust it On the entrance Based on this input, a specific output will be produced. An example of a function For example s (x), we tend to use the x symbol To express the entrance In the function And we use s to express the function Very often But we can use others For example s (x) equals x squared when x is an even number And it’s equal to x + 5 if x is an odd number What would happen if we inserted 2 on this function? And we express input 2 in the function Calculation method s (2) That is, we enter 2 in the function s And wherever we see S. We replace the xs In the number entered let’s try If 2 is the number of even, count 2 If 2 is an odd number, calculate 2 + 5 2 even number, so we calculate 2 squared 2 times 2 equals 4 What is s (3)? Again, we replace the variable with 3 We put 3 x place 3 times 3 if 3 is an even number, 3 + 5 if 3 is an odd number 3 is an odd number so we calculate 3 plus 5 It is equal to 8 Someone can ask This was an interesting way To define a method function for some type of these numbers But I could have done this using conventional equations In a way, especially if you allow Me using square brackets What the function could possibly do is my traditional toolkit Maybe it was not expressed? There are many forms and types of functions We can not use Q and Q We can use other symbols For example, m (p) equals the next largest number That begins with the letter w We will assume that we do business in English. For example, what is m (2)? 2 begins with What is the first number that follows and the first letter w? three Let’s try to calculate M (8) H of 8 is equal to? Eight starts with w And the number that follows and starts with b is thirteen And we see functions as a general method This conjugation m as we knew it The first letter in the literal expression of a number It starts in English. Let’s try something else Foolish thing. Not all functions appear Western Sometimes we deal with coupling Like y is equal to x plus 1 This is a coupling We can write r as a conjugation In terms of x, any s (x) equals x +1 And if we take an entrance For example, when x equals zero We take zero and add 1 You can add 1. Produces 1 S (2) is equal They tried to calculate it We can make a schedule And put the Senes in a column and the bumpers in a column When x equals 0, y equals 1 over there simple mistake S (2) equals 3 And overburden the table Sinat and antibiotics When x equals 0 y equals 1 When x equals 2 y is equal to 3 What is the purpose of using the pairing description here? Function notation says here S (x) equals x +1? The goal is to describe the equation in general An equation like this is not necessary Use the expression s (x) But it helps us understand The equation takes an input Ie x in this case and its transformation Converts it to x +1 Add to entry 1 Whatever the input port is greater than 1 From that original function. It’s natural to ask What is not an association Remember that we have said that pairing It produces only one exit for each entry The output is possible for this given input. For example– and let me look at it in a visual way From thinking about a function this time, or a relationship, This is the y-axis This is the x-axis And we’ll draw a radius of 2 Radius 2 This is minus 2 This is positive 2 This is minus 2 The circle is centered The radius is 2 This is the best attempt to draw a circle. Let me finish it So this is a circle The equation of this circle will be X squared plus y squared equals the squared radius That is equal to 4 This is the relationship between x and y That I expressed through this equation Here we draw all the xs and antigens to which the equation applies Is this the relationship between xenia and antibiotics? coupling? We can observe from seeing that it is not a conjugation Become a function If we choose a number x For example, x equals 1 There are two numbers y associated with x This p and this p We can solve by looking at the equation When x is equal to 1 it produces 1 squared plus y squared Equals 4 1 plus r squared equals 4 When we subtract 1 from both sides, r squared equals 3 Or y is equal to positive or negative root 3 This is positive for root 3 Here is a negative root of 3 So this relationship When we included 1 in the equation Produces positive 3 and root Minus 3 root together Therefore it is not a conjunction A single entry may not be related to two outputs In order to be a coupling for each input only one output

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