Y-axis

Definition

The y-axis is the vertical axis in a rectangular coordinate system, which represents the dependent variable and is typically used to plot the values or outcomes of a function. It is perpendicular to the x-axis and provides a visual reference for the range of values a function can take on.

5 Must Know Facts For Your Next Test

1. The y-axis is used to plot the values or outcomes of a function, which represents the dependent variable.
2. The y-axis is perpendicular to the x-axis and provides a visual reference for the range of values a function can take on.
3. The y-intercept of a linear function is the point where the function crosses the y-axis.
4. Transformations of functions, such as vertical shifts and compressions/expansions, are applied to the y-axis.
5. The y-axis is crucial in modeling linear functions, as it represents the output or dependent variable.

Review Questions

• Explain the role of the y-axis in the context of a rectangular coordinate system and how it relates to the representation of a function.
  • In a rectangular coordinate system, the y-axis represents the dependent variable of a function. It is perpendicular to the x-axis and provides a visual reference for the range of values the function can take on. The y-axis is used to plot the output or dependent variable, which is determined by the independent variable represented on the x-axis. This allows for the graphical representation of the relationship between the input and output of a function.
• Describe how the y-axis is used in the context of domain and range, and how it relates to the transformation of functions.
  • The y-axis is directly related to the range of a function, as it represents the set of possible output values. The domain, which is the set of possible input values, is represented on the x-axis. When transforming functions, such as through vertical shifts or compressions/expansions, the changes are applied to the y-axis, affecting the range of the function. This allows for the manipulation of the function's behavior and the exploration of its properties.
• Analyze the importance of the y-axis in the context of modeling linear functions and how it contributes to the understanding of the relationship between the independent and dependent variables.
  • $$ y = mx + b $$ In the equation for a linear function, the y-axis represents the dependent variable, which is the output or the variable that depends on the independent variable, $x$. The slope, $m$, determines the rate of change of the function, while the y-intercept, $b$, represents the point where the function crosses the y-axis. Understanding the role of the y-axis in the context of linear functions is crucial, as it allows for the modeling and analysis of the relationship between the input and output variables, which is essential for making predictions and drawing conclusions about the behavior of the system being studied.

Related terms

Rectangular Coordinate System: A two-dimensional coordinate system that uses perpendicular x-axis and y-axis to locate points in a plane.

Dependent Variable: The variable in a function that depends on the independent variable and is represented on the y-axis.

Domain and Range: The set of possible input values (domain) and output values (range) for a function.