Function

Definition

A function is a mathematical relationship between two or more variables, where one variable (the dependent variable) depends on the value of the other variable(s) (the independent variable(s)). Functions describe how changes in one quantity affect changes in another quantity.

5 Must Know Facts For Your Next Test

1. Functions can be represented in multiple ways, including equations, graphs, tables, and verbal descriptions.
2. The independent variable is the input value that the function depends on, while the dependent variable is the output value that the function calculates.
3. The domain of a function is the set of all possible input values, and the range is the set of all possible output values.
4. Linear functions have a constant rate of change, which means they can be graphed as a straight line.
5. The slope of a linear function represents the rate of change, and the y-intercept represents the starting value of the function.

Review Questions

• Explain how the concept of a function relates to the topic of graphing linear equations.
  • When graphing linear equations, the equation represents a function that describes the relationship between the independent variable (typically the x-coordinate) and the dependent variable (typically the y-coordinate). The graph of a linear equation is a straight line, which is the visual representation of the function. The slope and y-intercept of the line are important characteristics of the linear function, as they determine the rate of change and starting value, respectively.
• Describe how the domain and range of a function relate to the graph of a linear equation.
  • The domain of a linear function represents the set of all possible input values, which corresponds to the x-coordinates on the graph. The range of a linear function represents the set of all possible output values, which corresponds to the y-coordinates on the graph. The domain and range of a linear function are typically unlimited, meaning the function can take on any real number as an input or output, resulting in a graph that extends indefinitely in both the positive and negative directions.
• Analyze how the characteristics of a linear function, such as slope and y-intercept, affect the graph of the function.
  • The slope of a linear function determines the rate of change between the independent and dependent variables. A positive slope indicates the function is increasing, a negative slope indicates the function is decreasing, and a zero slope indicates the function is constant. The y-intercept of a linear function represents the starting value of the function, which is the point where the graph of the function intersects the y-axis. Together, the slope and y-intercept define the unique characteristics of a linear function and how it is represented on a graph.

Related terms

Domain: The set of all possible input values for a function.

Range: The set of all possible output values for a function.

Linear Function: A function that has a constant rate of change, represented by a straight line graph.