How does an equation represent a function?

Answer 1

An equation in this context usually has two variables, let's say x and y. A function in this case usually has one variable as an input let's say x. f(x) is the output of the expression that defines the function.

There are some criteria of a function that equations do not have. Functions must only have one output per input, basically, if you draw a vertical line anywhere on the graph, the line must only intersect at one point.

So how does an equation represent a function? We can use the second variable in the equation to represent the output of the function and isolate f(x)

Examples:

x+ 3y = 10

x + 3f(x) = 10

3f(x) = 10 - x

f(x) = (10-x)/3

x+ 3y = 10 represents f(x) = (10-x)/3

Trying x^2+y^2=9 would not work, because isolating for y we would get and equation of y = (plus or minus)sqrt(9-x^2) which does not follow the criteria of a function.

Hope it helped!