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Example: Determining if a Graphed Straight Line and a Horizontal Parabola Represent a Function Using the Vertical Line Test
To determine whether a graph represents a mathematical function, apply the vertical line test. For example, consider the graph of a slanted straight line. Because any vertical line drawn anywhere on the coordinate plane intersects this straight line at exactly one point, the graph passes the test and represents a function. In contrast, consider the graph of a sideways parabola that opens to the right (a horizontal parabola). A vertical line can be drawn that passes through two distinct points on this curve. Because a single vertical line intersects the graph more than once, it indicates that one -value corresponds to multiple -values. Therefore, the horizontal parabola fails the vertical line test and does not represent a function.
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Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
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Example: Determining if a Graphed Straight Line and a Horizontal Parabola Represent a Function Using the Vertical Line Test
Example: Determining if a Graphed Vertical Parabola and a Circle Represent a Function Using the Vertical Line Test
Example: Determining if a Graphed Ellipse and a Slanted Line Represent a Function Using the Vertical Line Test
Example: Verifying the Graph of the Equation is a Function
A data analyst is reviewing a graph that tracks a machine's power consumption over a 24-hour period. To verify if the consumption is a mathematical function of time, the analyst applies the vertical line test. According to this test, the analyst should conclude the graph does not represent a function if which of the following occurs?
A laboratory technician is analyzing a graph that represents the reaction rate of a chemical compound over various temperatures. To determine if the reaction rate is a mathematical function of the temperature, the technician applies the vertical line test. Match each observation from the test with the correct conclusion about the relationship shown on the graph.
An operations manager is using a graph to track the relationship between factory output and energy consumption. True or False: According to the Vertical Line Test, this graph represents a mathematical function if every vertical line drawn on the coordinate plane intersects the graph at most once.
Interpreting Sensor Data with the Vertical Line Test
A business analyst is reviewing a chart mapping daily marketing spend to sales revenue. To visually confirm whether the graph represents a mathematical function, the analyst applies the vertical line test. For the graph to pass this test and be considered a function, any vertical line drawn on the coordinate plane must intersect the graph at a maximum of ____ point(s).
Learn After
A quality control technician is inspecting a manufactured part with an edge that follows the shape of a horizontal parabola (a curve that opens to the side). When plotting this shape on a coordinate grid, why is it determined that the graph fails the vertical line test?
A technician at a manufacturing facility is examining data plots of different machine components to determine if they represent mathematical functions. Match each component's graphed shape with the correct conclusion based on the vertical line test.
A drafting technician is reviewing a blueprint that includes a component's edge shaped like a horizontal parabola (a curve that opens to the side). True or False: This shape represents a mathematical function because it passes the vertical line test.
Quality Control and the Vertical Line Test
A technical designer is evaluating a graph of a sideways curve, also known as a horizontal parabola. To determine if this graph represents a mathematical function, the designer applies the vertical line test. The graph is determined not to be a function because at least one vertical line can be drawn that intersects the curve at ____ distinct point(s).