Final answer:
In mathematics, a function describes a relationship between two quantities. It can be represented in multiple ways, including tables, graphs, and equations. Understanding these multiple representations is relevant as they provide different ways to analyze and understand the relationship between the quantities.
Step-by-step explanation:
In mathematics, a function describes a relationship between two quantities. It maps each input value to a unique output value. Functions can be represented in multiple ways, including tables, graphs, and equations.
The table representation lists the input values and their corresponding output values.
The graph representation shows the relationship between the two quantities on a coordinate plane. The x-axis represents the input values, and the y-axis represents the output values.
The equation representation uses mathematical expressions to define the relationship between the input and output values. The equation can be solved for the output value given an input value.
For example, let's consider the function y = 2x. In table representation, if x is 1, y is 2; if x is 2, y is 4; if x is 3, y is 6, and so on. In graph representation, the points (1, 2), (2, 4), (3, 6), and so on lie on a straight line. In equation representation, we can plug in an input value to calculate the corresponding output value.
Understanding these multiple representations of functions is relevant because they provide different ways to analyze and understand the relationship between the two quantities. Each representation offers unique insights and can be used to solve various problems.