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Section 1.2.5 Class Activity You have many characteristics that you can describe about graphs and functions using the questions that you began developing in Lesson 1.2.1. You also have learned how
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01
Identify the x-intercepts by setting the function equal to zero and solving for x.
02
Identify the y-intercept by evaluating the function at x=0.
03
Determine the symmetry of the function by checking if f(x) = f(-x) for all x.
04
Find the domain of the function, which is the set of all possible input values that produce real output values.
05
Determine the range of the function, which is the set of all possible output values that result from the input values in the domain.
06
Identify any asymptotes (vertical, horizontal, or slant) by analyzing the behavior of the function as x approaches certain values.

Who needs characteristics of function graphs?

01
Students studying calculus or precalculus.
02
Math teachers who are teaching about functions and their characteristics.
03
Engineers or scientists analyzing data using mathematical models.
04
Anyone working with graphs and functions in their profession or research.

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Characteristics of function graphs generally refer to key features such as intercepts, asymptotes, domain and range, symmetry, and behavior at infinity that visually and mathematically describe the function.
Individuals or entities that are engaged in mathematics education, research, or analysis may be required to file characteristics of function graphs, particularly in academic or professional contexts.
To fill out characteristics of function graphs, one should identify and detail each graph's critical points, evaluate limits, determine asymptotic behavior, and summarize domain and range, typically in a structured report or form.
The purpose of characteristics of function graphs is to provide a comprehensive overview of the behavior and properties of a function, aiding in its analysis, comparison, and application in various fields.
Information required typically includes the function's equation, intercepts, critical points, asymptotes, domain and range, and a general description of the graph's shape and continuity.
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