SOLUTION: what makes a function special as it relates to all other relation

Question 477971: what makes a function special as it relates to all other relation
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x is the independent variable
y is the dependent variable.
for every value of x, there is one and only 1 value of y.
y = x^2 would be a function
graph of that looks like this:

you can see that for each value of x there is one and only one value of y .
y^2 = x would be a relation.
solve for y to get y = +/- sqrt(x).
if any one value of x results in more than one value of y, the equation is a relation rather than a function.
in this particular case, almost every value of x results in more than one value of y as shown in the graph below:

you can see that at x = 0, there is only one value of y which is also 0.
for every other value of x for which there is a corresponding value of y, you can see that there are 2 values of y.
that makes the equation of y = +/- sqrt(x) a relation rather than a function.
that's the difference between a relation and a function.
the function has one and only one value of y for each value of x.
the relation can have more than one value of y for any value of x that that creates a value of y.
this assume x is in the domain and y is in the range.
you give the equation the vertical line test.
if only one value y intersects with the vertical line, then you have a function.
if more than one value of y intersect with the vertical line, then you have a relation.
the vertical line test has to be done for every value of x in the domain.

RELATED QUESTIONS
Pythagorean triplets represent a special relation that both satisfy the Pythagorean... (answered by Edwin McCravy,Alan3354)

The relation between the cost of a certain gem and its weight is linear. In looking at... (answered by Boreal)

What Makes A Quadratic Function Equation diffrent from other... (answered by Edwin McCravy)

Consider the relation given by ( - 1, 0), (2, - 1), ( - 2, 1), (0, 3). a)... (answered by Boreal)

Jake earns $7.50 per hour working at a local car wash. The function, ƒ(x) = 7.50x,... (answered by Boreal)

a ball is thrown from a 180m high cliff> the relation h=-5t^2-5t+180 relates the time in... (answered by nerdybill)

middle school algebra- what is the definition for natural domain as it relates to... (answered by midwood_trail)

I need help please. The function that relates weight in grams of a crystal (w) to the... (answered by checkley71)

In the North Chicago area, an 820-square-foot apartment rents for $1510 per month. A... (answered by josmiceli)