What does it mean when functions are equal?
Two functions are equal if they have the same domain and codomain and their values are the same for all elements of the domain.
How do you prove that a function is equal?
The set A is called the domain of f and the set B is called the codomain. We say two functions f and g are equal if they have the same domain and the same codomain, and if for every a in the domain, f(a)=g(a).
Do equal functions have the same graph?
I know that, Identical Functions (Equal Functions) are those functions which have the same domain and give the same output for every input value. These functions have the same graph.
How do you determine a function?
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
How do we evaluate a function?
Evaluating a function means finding the value of f(x) =… or y =… that corresponds to a given value of x. To do this, simply replace all the x variables with whatever x has been assigned. For example, if we are asked to evaluate f(4), then x has been assigned the value of 4.
Can the same function be represented by different formulas?
But as you note, if two different formulas for the right hand side actually give the same values when you substitute values from the domain, then the functions so defined will be the same. (,) is a binary operation on functions; it’s defining property is (g,h)(x)=(g(x),h(x)).
Which relation describes a function?
A function is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.” The input values make up the domain, and the output values make up the range.
Which relation is a function?
A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to.