Finding the Function of a Given Graph

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To find the function of a given graph based on the points (0,0), (1,-0.7568), (2,0.99061), and (3,-0.988), graphing the points is essential. If the graph appears linear, the equation can be determined using y=mx. For curves resembling parabolas, plotting y against x² or y against x³ may help identify the function. The discussion suggests that the graph is likely not linear and may be trigonometric due to the alternating signs of the y-values. Finding the exact function by hand can be challenging, especially for trigonometric functions, but using a calculator or software for a line of best fit is recommended.
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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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