Y-Axis

Definition

The y-axis is the vertical axis on a coordinate plane, perpendicular to the horizontal x-axis. It is used to represent and measure the vertical or up-down position of a point or object in a two-dimensional space.

5 Must Know Facts For Your Next Test

1. The y-axis represents the vertical position or height of a point on a coordinate plane.
2. The y-coordinate of a point on the coordinate plane corresponds to the value on the y-axis.
3. The range of a function is the set of all possible y-values, or the vertical extent of the function's graph.
4. Exponential functions have graphs that are curved and open upward or downward, with the y-axis playing a crucial role in determining the rate of growth or decay.
5. Rotating the axes of a coordinate plane involves changing the orientation of the x-axis and y-axis, which can affect the representation and interpretation of data.

Review Questions

• Explain how the y-axis is used to determine the domain and range of a function.
  • The y-axis is essential in determining the domain and range of a function. The domain represents the set of input values, which are plotted along the x-axis. The range, on the other hand, represents the set of output values, which are plotted along the y-axis. The range of a function is the vertical extent of its graph, as it shows the minimum and maximum y-values the function can take. Understanding the role of the y-axis in representing the range is crucial for analyzing the behavior and characteristics of a function.
• Describe the importance of the y-axis in the graphs of exponential functions.
  • The y-axis plays a critical role in the graphs of exponential functions. Exponential functions have a characteristic curved shape that opens upward or downward, depending on the function's growth or decay rate. The y-axis represents the dependent variable, which in the case of exponential functions, can grow or decay rapidly. The y-axis scale and the function's rate of change (the exponent) determine the steepness and shape of the exponential graph, providing valuable insights into the function's behavior and its practical applications.
• Analyze how the rotation of axes in a coordinate plane can affect the interpretation of the y-axis.
  • Rotating the axes of a coordinate plane involves changing the orientation of the x-axis and y-axis. This can significantly impact the interpretation of the y-axis and the representation of data. When the axes are rotated, the y-axis may no longer represent the vertical position or height of a point, but instead, it may represent a different measure or characteristic of the data. Understanding how the rotation of axes affects the y-axis is crucial for correctly interpreting and analyzing the information presented in the transformed coordinate plane.

Related terms

Coordinate Plane: A two-dimensional plane with perpendicular x and y axes used to represent and plot points and functions.

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

Exponential Function: A function where the independent variable appears as an exponent, resulting in rapid growth or decay.