Finding the Function of a Given Graph

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SUMMARY

The discussion focuses on determining the function of a graph based on given coordinate points: (0,0), (1,-0.7568), (2,0.99061), and (3,-0.988). Participants suggest graphing the points to identify the function type, recommending methods such as using the equation of a line (y=mx) for linear functions or exploring parabolic relationships by plotting y against x². The consensus indicates that the function is likely non-linear and may involve trigonometric components due to the alternating signs of the y-values. Advanced tools or calculators are recommended for finding the line of best fit.

PREREQUISITES
  • Understanding of coordinate geometry and graphing techniques
  • Familiarity with linear equations and their forms, specifically y=mx
  • Basic knowledge of polynomial and trigonometric functions
  • Experience with graphing calculators or software for curve fitting
NEXT STEPS
  • Learn how to perform polynomial regression using tools like Python's NumPy library
  • Explore trigonometric functions and their properties for modeling periodic data
  • Study methods for determining the line of best fit using statistical software
  • Investigate the use of graphing calculators for visualizing complex functions
USEFUL FOR

Students, mathematicians, and data analysts who are involved in graph analysis, function approximation, or anyone seeking to understand the relationship between data points in a graphical format.

lch7
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You are given a table and (maybe) a picture of a graph. Here are the points given: 0,0; 1,-.7568; 2,.99061; and 3,-.988. What is the function? Is it possible to figure out by hand?
 
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lch7 said:
You are given a table and (maybe) a picture of a graph. Here are the points given: 0,0; 1,-.7568; 2,.99061; and 3,-.988. What is the function? Is it possible to figure out by hand?

Call the first co-ordinate x, and the second y in each case.
Graph the points. If it is a straight line, use y=mx to find the equation.

If it it curves up like a parabola, try graphing y vs x2 and or y = y vs x3

If the graph flattens off, try y vs √x etc.
 
If you have a good calc or program, do line of best fit. It is not linear. It very well may be trigonometric due to the alternating signs. There are ways to do it for EXPO and poly but Trig ones are hard by hand.
 

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