Learn Before
Example: Graphing the Function
To actively graph the absolute value function , purposefully select a range of both positive and negative -values to substitute into the equation. For instance, directly evaluating the integers from to yields the corresponding ordered pairs , , , , , , and . Plotting these specific coordinates on a geometric graph and connecting the successive points definitively reveals a symmetrical V-shaped graph possessing its vertex purely at the origin , physically demonstrating that all corresponding output values are non-negative.
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Intermediate Algebra @ OpenStax
Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
Algebra
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.
Learn After
Example: Graphing the Function
A machinist is programming a CNC router to cut a symmetrical V-shaped groove defined by the function . Based on the standard properties of this function, at what coordinate point on the machine's grid will the 'vertex' (the lowest point of the groove) be located?
To graph the absolute value function , a student must follow several steps. Arrange the following actions in the correct order to successfully plot the function based on the procedure described.
In a manufacturing quality control process, a technician uses the absolute value function to calculate the deviation of a part's measurement from the standard. Based on the properties of this function, match each term with its corresponding output or characteristic.
A quality control technician uses the absolute value function to calculate the deviation of a component's width from the standard. True or False: Based on the properties of this function, all output values plotted on the graph will be non-negative.
During a technical training session on blueprint reading, an apprentice is mapping out basic mathematical models used in part design. When plotting the coordinates for both positive and negative values of the function , the resulting graph creates a symmetrical ____-shaped pattern.