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When is a relation considered to be function?
A relation is a function when an x value only has one y value associated with it. An easy way to tell this is to graph the relation, then draw a vertical line through it. If, at any point, it touches the graph twice, the relation isn't a function.
What is a one-to-one relation in mathematics?
A one-to-one relation in math means that for every value in the range, there's at most one value that maps to it. If you think of relations as people sitting on a bus, this means that no one is sharing a seat. More often, mathematicians talk about one-to-one functions (formally called injections) - these are just one-to-one relations that happen to be functions :-). If we write the function as y=f(x), the condition for it being one-to-one is that if f(a)=f(b), then a=b. When looking at the graph of a relation, we can determine if it's one-to-one by the horizontal line test: if any horizontal line drawn on the graph intersects the relation at most once, it is one-to-one. On the other hand, if a horizontal line intersects the relation twice, the relation is not one-to-one. For example, y=x^2 is not a one-to-one relation: (-1)^2 and 1^2 both get mapped to 1. We can see this in the graph of y=x^2 because a horizontal line above the x-axis will intersect the graph twice. y=x^3, on the other hand, is a one-to-one relation. Because the cube of a negative number stays negative, no two numbers get sent to the same number by cubing them.
What is a line that intersects a circle twice?
a chord
What is the line that intersects a circle twice?
It is called a secant line
When the graph of a quadratic function crosses the x-axis twice the x-coordinate of the lies exactly halfway between the two x-intercepts?
Exactly halfway
