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Example: Finding Domain and Range from the Graph of a Function (Variant 1)
Consider a function whose graph is a curved line segment passing through the points , , and . To find its domain, observe all the -values that correspond to a point on the graph; the curve spans horizontally from to , so the domain is written in interval notation as . To find its range, examine all the -values associated with the graph; the curve spans vertically from its lowest point at to its highest point at , making the range .
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Intermediate Algebra @ OpenStax
Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
Algebra
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Example: Finding Domain and Range from the Graph of a Function (Variant 1)
Example: Finding Domain and Range from the Graph of a Function (Variant 2)
A quality control technician is using a graph to track the temperature of a machine over an eight-hour shift. According to the visual method for determining the range of a function from its graph, which action confirms that a specific temperature value is included in the range?
A network administrator is reviewing a graph that shows the latency (in milliseconds) of a server over a 24-hour period. To find the range of latency values, the administrator must determine which millisecond levels were recorded by the system. Arrange the following steps in the correct order to visually confirm if a specific latency value is part of the function's range.
Identifying the Axis for Sales Range
A laboratory technician is interpreting a graph that shows the concentration of a chemical over an eight-hour shift. Match each component of the visual process for finding the range of the concentration function with its correct role.
A logistics manager is analyzing a graph that models the daily delivery costs (-values) for a fleet of trucks. True or False: To verify if a specific cost amount is included in the range of the function, the manager should visually follow that -value left or right horizontally to see if the path intersects the graph.
Learn After
An industrial technician is monitoring the output of a pressure sensor during a machine's operation cycle. The output is graphed as a curved line segment passing through the coordinates , , and . Based on the definition of domain as the set of all possible input values (-values), which interval represents the domain of this function?
A laboratory technician is recording the voltage variance of a sensor during a calibration cycle. The results are displayed on a graph as a curved segment passing through the points , , and . Match each mathematical term to the interval that correctly represents the data set for this specific graph.
A maintenance technician uses a diagnostic tool to graph the efficiency of a motor during a test cycle. The resulting graph is a curved segment passing through the points , , and . The domain of this efficiency function, representing the set of all possible input values (-values), is the interval .
An industrial technician is monitoring the performance of a hydraulic pump. The diagnostic software displays the pump's pressure variance as a curved line segment passing through the coordinates , , and . The technician identifies that the vertical span of the graph, which covers all possible output values from to , represents the interval . This complete set of output values (the -values) is mathematically defined as the ____ of the function.
A medical lab technician is tracking the temperature variance of a sensitive sample during a controlled cooling cycle. The results are plotted on a graph as a curved segment passing through the coordinates , , and , where the vertical axis represents the temperature in degrees. Arrange the following steps in the correct order to identify the range of this temperature function.