What is a Function in Algebra
To find the area of a square we need the length of the side. So, we can say that the area of the square depends on the length of the side of the square. It means that if the length of the side changes, the area also changes then we can say that the first is the function of the other. So, we can conclude that the area of the square is the function of and it depends on the length of its side. So, in mathematics algebraic functions can be defined as, a relationship between two variables something like ‘x’ and ‘y’ , function if there is a rule which assigns to each value of the variable ‘x’ there exists one and only one value of ‘y’. Then we can say that y is a function of x.
It is clear now that a function must be single valued, for instance, y=3x+2. Here to each value of x there is a unique value of y. All the values which x can assume is called the domain. These are the values for which the function can be defined. In the function y=3x+2, the domain include all the real numbers which means ‘x’ can be any real number.
Is this topic how to do algebra problems hard for you? Watch out for my coming posts.
Once the domain is defined, the set of corresponding ‘y’ values for each value of ‘x’ is called the range of the function. For instance, if x=2 in the domain then y=(3.3)+2=11 is the corresponding value in the range. So, ‘x’ can be called the independent variable and ‘y’ a dependent variable as its value depends on the value of x.
Consider an example of a algebra functions given by, x={-1,0,1,2} where each value is the value of the domain, the rule being y=x2-1. Let us write the ordered pair of the given function. Here we need to plug in each of the values of ‘x’ in the given rule to arrive to the corresponding ‘y’ value of the range. When x=-1 then y=(-1)2-1 = 1-1=0; when x=0 then y=(0)2-1=-1; when x=1 then y=(1)2-1=0; when x=2 then y=(2)2-1=4-1=3. So, when the domain= {-1,0,1,2} the corresponding values of the range={0,-1,0,3} and the ordered pair of the function is (x,y)={(-1,0),(0,-1),(1,0),(2,3)}. So, functions algebra is a well behaved relation which means given an ‘x’ there is exactly one and only one ‘y’.
In the above functions algebra each ‘x’ to each ‘y’ we can see that there is only one arrow coming from each of ‘x’ of the domain and hence it is a function.
To find the area of a square we need the length of the side. So, we can say that the area of the square depends on the length of the side of the square. It means that if the length of the side changes, the area also changes then we can say that the first is the function of the other. So, we can conclude that the area of the square is the function of and it depends on the length of its side. So, in mathematics algebraic functions can be defined as, a relationship between two variables something like ‘x’ and ‘y’ , function if there is a rule which assigns to each value of the variable ‘x’ there exists one and only one value of ‘y’. Then we can say that y is a function of x.
It is clear now that a function must be single valued, for instance, y=3x+2. Here to each value of x there is a unique value of y. All the values which x can assume is called the domain. These are the values for which the function can be defined. In the function y=3x+2, the domain include all the real numbers which means ‘x’ can be any real number.
Is this topic how to do algebra problems hard for you? Watch out for my coming posts.
Once the domain is defined, the set of corresponding ‘y’ values for each value of ‘x’ is called the range of the function. For instance, if x=2 in the domain then y=(3.3)+2=11 is the corresponding value in the range. So, ‘x’ can be called the independent variable and ‘y’ a dependent variable as its value depends on the value of x.
Consider an example of a algebra functions given by, x={-1,0,1,2} where each value is the value of the domain, the rule being y=x2-1. Let us write the ordered pair of the given function. Here we need to plug in each of the values of ‘x’ in the given rule to arrive to the corresponding ‘y’ value of the range. When x=-1 then y=(-1)2-1 = 1-1=0; when x=0 then y=(0)2-1=-1; when x=1 then y=(1)2-1=0; when x=2 then y=(2)2-1=4-1=3. So, when the domain= {-1,0,1,2} the corresponding values of the range={0,-1,0,3} and the ordered pair of the function is (x,y)={(-1,0),(0,-1),(1,0),(2,3)}. So, functions algebra is a well behaved relation which means given an ‘x’ there is exactly one and only one ‘y’.
In the above functions algebra each ‘x’ to each ‘y’ we can see that there is only one arrow coming from each of ‘x’ of the domain and hence it is a function.
