Understanding f(x) and y in the function f(x) = x² + 4: Explained

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SUMMARY

The discussion clarifies the relationship between the function notation f(x) = x² + 4 and the equation y = x² + 4. It establishes that f(x) represents a function assigning values based on input x, while y = f(x) is an equation that can be graphed on a Cartesian plane. The correct interpretation requires defining y as f(x) to ensure clarity in mathematical communication. This distinction is crucial for accurately visualizing the properties of the function.

PREREQUISITES
  • Understanding of function notation in mathematics
  • Familiarity with Cartesian coordinate systems
  • Basic knowledge of graphing quadratic functions
  • Concept of variable assignment in equations
NEXT STEPS
  • Study the properties of quadratic functions and their graphs
  • Learn about function transformations and their effects on graphs
  • Explore the concept of function composition and its applications
  • Investigate the differences between functions and relations in mathematics
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Students learning algebra, educators teaching mathematics, and anyone interested in understanding the fundamentals of functions and their graphical representations.

thomas49th
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When you say f(x) = x² + 4 (the function of f is defined at x² + 4)
is that the same as saying y = x² + 4?
 
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Only if you set y=f(x). f(x) is a function assigning the value f(x) to each input x. y = f(x) is just an equation, which can be graphed on a Cartesian plane; it is a method of visualizing the properties of the function.
 
thomas49th said:
When you say f(x) = x² + 4 (the function of f is defined at x² + 4)
is that the same as saying y = x² + 4?
Did you mean "defined as [itex]x^2+ 4[/itex].

No, that is NOT the same as saying "y= [itex]x^2+ 4[/itex]" unless, as slider142 said, you define y= f(x). If you are graphing such a function on an standard "xy coordinates sytem" then the first thing you should say is "let y= f(x)". That is so standard that it is not always said.
 

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