Modeling Discrete Data: Quiz

Problem 2

Consider the curve

Which of the following points lie on the curve? Of the points that do not, which lies furthest (measured vertically) from the curve?

  1. (–1, –16)
  2. (–4, –13)
  3. (3, 2)
  4. (0, –1)
  5. (5, –6)

Answers, problem 2

All we have to do here is to plug in the values of x of the given ordered pairs and compare the value of c(x) to the value of the corresponding y value. We then find the absolute difference between c(x) and the y value corresponding to x. If this difference is equal to 0, then the point in question lies on the curve, if not, the point does not lie on the curve and we note the value of the difference. The point with the largest difference is the point that lies furthest verically from the curve.
  1. c(–1) = –6; Distance = 10
  2. c(–4) = –33; Distance = 20: this is the largest
  3. (3, 2) is on the curve
  4. (0, –1) is on the curve
  5. (5, –6) is on the curve
Therefore we can see that all points 3, 4 and 5 lie on the curve while point 2 lies furthest vertically from the curve.

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