Domain of f(x) from -9 to 10 - Pre-calc Function

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SUMMARY

The domain of the function f(x) = √(x² - 3x + 2) is defined using interval notation as [-9, 10]. This conclusion is reached by analyzing the quadratic expression under the square root, which must be non-negative for the function to yield real values. The discussion clarifies that the domain does not encompass all real numbers, as negative values would result in complex outputs. Therefore, the correct interpretation of the domain is limited to the specified interval.

PREREQUISITES
  • Understanding of quadratic functions and their properties
  • Knowledge of interval notation
  • Familiarity with real-valued functions
  • Basic graphing skills, particularly with calculators
NEXT STEPS
  • Study the properties of quadratic functions and their graphs
  • Learn about interval notation and its applications in mathematics
  • Explore the concept of real-valued functions and their domains
  • Practice graphing functions using graphing calculators or software
USEFUL FOR

Students studying pre-calculus, educators teaching function analysis, and anyone seeking to understand the domain of real functions.

litz
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i was wondering, it says use interval notation to describe the domain of the real function, but a real function means the domain is a set of real numbers. does it mean all real numbers? i graphed it on my calculator and got [-9,10] but i have no idea if i should have negative infinity to positive infinity for all real numbers??

f(x)=square root of (x squared -3x+2). what's the domain!? :confused:
 
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Start small. Consider the function [itex]f(x)=\sqrt{x}[/itex]. If the function is to be real-valued, then what sort of numbers aren't we allowed to put in for x?
 

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