How can I write a function that describes a relationship between two quantities, and what are some examples?

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Vasquez · Accepted Answer

Example Question:f(x) is a linear function defined on the set of real numbers. Four values of f are given in the following table: x―f(x)―13410678410Give the definition for f(x).Explanation:By the two-point formula, the equation of a line through points (x1,y1),(x2,y2) isy−y1=m(x−x1)where m=x2−x1y2−y1, the slope of the line. The choice of the two points from the given four is arbitrary, so we will select the middle two ordered pairs. Substituting x1=10,y1=6,x2=7,y2=8, thenm=x2−x1y2−y1=7−108−6=−32The first formula becomesy−10=−32(x−6)Since f(x)=y solve for y. First, distribute −32 throughout the difference at right:y−10=−32x−(−32)6y−10=−32x−(−9)y−10=−32x+9Isolate y by adding 10 to both sides:y−10+10=−32x+9+10y=−32x+19Replacing, the definition of f(x) isf(x)=−32x+19

How can I write a function that describes

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