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.
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The y-axis represents the vertical position or height of a point on a coordinate plane.
The y-coordinate of a point on the coordinate plane corresponds to the value on the y-axis.
The range of a function is the set of all possible y-values, or the vertical extent of the function's graph.
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.
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 When the axes are rotated, the y-axis may no longer represent the vertical position or height of a point, but instead, it may represent a different measure or characteristic of the data.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.