Question

A series of points in the form (x, y) is a function if every
A graph is a function if a vertical line passes through the graph at most
-value is different.
time.

Answer 1

- 1

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain) where each input is related to exactly one output. This means that for each input value in the domain, there is only one corresponding output value in the codomain.

- 2

One way to determine if a series of points is a function is by checking if each input value (x-coordinate) corresponds to only one output value (y-coordinate). If there are multiple y-values for the same x-value, then the series of points is not a function.

- 3

Additionally, a graph is a function if a vertical line can pass through the graph at most one time. This is known as the vertical line test. If a vertical line intersects the graph in more than one point, then the graph is not a function.

- 4

Overall, the key idea is that in a function, each input value must have a unique output value. This principle is important in various areas of mathematics, including calculus, algebra, and statistics.