A function
one value for "Y" for every "X" is related by a function... it cannot be a function if it has more than one Y value for an X value
A graph is represents a function if for every value x, there is at most one value of y = f(x).
Assuming that y is a function of x, that follows from the definition of a function. For each x-value, there can only be one y-value. The definition of a function is that (in this case), for every value of "x", a value of "y" can be calculated unambiguously. In the more general case, for every combination of the independent variables, a single value for the dependent variable can be calculated unambiguously.
When each x value has only one y value, the relation is classified as a function. In a function, for every input (x), there is a unique output (y), ensuring that no x value is paired with multiple y values. This characteristic is crucial for determining the validity of a mathematical function, making it predictable and consistent.
A Function
A function
one value for "Y" for every "X" is related by a function... it cannot be a function if it has more than one Y value for an X value
one value for "Y" for every "X" is related by a function... it cannot be a function if it has more than one Y value for an X value
one value for "Y" for every "X" is related by a function... it cannot be a function if it has more than one Y value for an X value
A graph is represents a function if for every value x, there is at most one value of y = f(x).
A function is a rule which assigns exactly one output f(x) to every input x.
A function is an equation (a relation) which has only one y-value for every x-value. If a single x-value has more than one y-value, the equation is no longer called a function.
If we are talking about a linear equation in the form y = mx + b, then all linear equations are functions. Functions have at most one y value to every x value (there may be more than one x value to every y value, and some x- and y-values may not be assigned at all); all linear equations satisfy this condition.Moreover, linear equations with m ≠ 0 are invertible functions as well, which means that there is at most one x-value to every y-value (as well as vice versa).
Assuming that y is a function of x, that follows from the definition of a function. For each x-value, there can only be one y-value. The definition of a function is that (in this case), for every value of "x", a value of "y" can be calculated unambiguously. In the more general case, for every combination of the independent variables, a single value for the dependent variable can be calculated unambiguously.
how about X = X
When each x value has only one y value, the relation is classified as a function. In a function, for every input (x), there is a unique output (y), ensuring that no x value is paired with multiple y values. This characteristic is crucial for determining the validity of a mathematical function, making it predictable and consistent.
A Function