All functions are relations but not all relations depict functions.
To determine whether a relation represented in ordered pairs and table of values a
function or not, just observe its x-values. If there is no repetition on the x- values, then it's a
function otherwise, it is not.
If the relation is expressed in mapping diagram, the one-to-one and many- to-one
correspondence only illustrate a function. The one-to-many and many-to-many are not.
The relations when expressed in equation/rule, for every specific value of x, there
should only be one corresponding y-value for that x-value. For example, y = x
+ 10, is a function because y will always be ten greater than x. Equations with exponents can
also be functions. For example, y = x2-4 is a function; although x-values of 2 and -2 give the
same y-value of zero (0), that is only possible y-value for each of those x-values. However,
y2 = x + 1 is not a function because if you assign x-value of 8, y has two possible values
which are 3 and -3. Expressing it in ordered pairs, (8,3) and (8, -3). Looking at these ordered
pairs, there is a repeated value in x.
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