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Constant Function
A constant function is mathematically defined by the basic equation , where can be any real number. When graphed on the rectangular coordinate plane, it exclusively forms a perfectly straight horizontal line that continuously crosses the vertical axis exactly at the -intercept . Because absolutely any given real number can serve securely as a valid input, its structured domain broadly spans . Conversely, since the function rigidly returns the exact same value identically every single time, its calculated range strictly consists of that isolated singular number .
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OpenStax
Intermediate Algebra @ OpenStax
Algebra
Ch.10 Exponential and Logarithmic Functions - Intermediate Algebra @ OpenStax
Related
Example: Graphing the Function
Example: Graphing the Function
Example: Graphing the Function
Reading the Domain of a Function from its Graph
Reading the Range of a Function from its Graph
Example: Reading the Domain and Range from the Graph of a Function
Example: Reading Function Values, Intercepts, Domain, and Range from a Graph
Constant Function
Square Function
Example: Comparing the Graphs of and
Example: Reading Function Values, Intercepts, Domain, and Range from a Graph (Variant 1)
A service technician uses a function to calculate the total repair cost based on the number of hours () worked. To analyze the billing data, the technician views the function's graph. Match each mathematical term with its correct description in the context of this graph.
In the graph of a mathematical function , the -coordinate of any point on the graph can be represented by the function notation .
A project manager uses a function to model the total production cost of a specific part, where represents the number of units produced. When the manager looks at the graph of this function on a coordinate plane, what does the value represent for any point on the graph?
Visualizing Industrial Data
A business analyst is using a mathematical function to model a company's weekly shipping costs. When this function is plotted on a coordinate system, the resulting graph serves as a visual representation of all the function's ordered ____, which can be written in the form to show the relationship between a specific week and its cost.
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As a warehouse manager, you use a business inventory software that charges a flat monthly fee of 500 dollars, regardless of how many inventory items you log. This pricing model is an example of a constant function, mathematically defined by the equation . Based on the definition of a constant function, what does its graph exclusively look like on a rectangular coordinate plane?
Suppose a professional consulting firm charges a flat monthly retainer fee of dollars, regardless of how many hours () are worked. This pricing model is represented by the constant function . Match each mathematical property of this constant function with its correct description.
A corporate facility manager pays a flat monthly fee of 800 dollars for security services, regardless of how many times the alarm is triggered. This is modeled by the constant function . Because the function always returns the same output value for any input, its ____ consists strictly of the single value 800.
A corporate security firm charges a flat monthly service fee of 150 dollars, which is represented by the constant function . True or False: On a rectangular coordinate plane, the graph of this function will intersect the vertical axis at the point .
Fixed Software Licensing Costs