Question

1. the following table contains a sample of data collected from the deep - ocean assessment and reporting of tsunamis (dart) program. what domain and range issues must you consider to make a scatterplot on your graphing calculator? 2. make the scatterplot on your calculator and record it here. does the graph appear to show a horizontal or vertical shift?

Explanation:

Step1: Determine the domain

The domain is the set of all input values (here, the depth of the ocean \(d\)). Looking at the data: \(d = 9,25,49,81,121\). The minimum value of \(d\) is \(9\) and the maximum is \(121\). So, for the graphing calculator, we need to set the \(x -\)min (lower - bound of the domain) to a value less than or equal to \(9\) (e.g., \(x-\text{min}=0\)) and \(x-\)max (upper - bound of the domain) to a value greater than or equal to \(121\) (e.g., \(x - \text{max}=150\)).

Step2: Determine the range

The range is the set of all output values (here, the speed of the wave \(s\)). Looking at the data: \(s=9.3,15.5,21.7,27.9,34.1\). The minimum value of \(s\) is \(9.3\) and the maximum is \(34.1\). So, for the graphing calculator, we need to set the \(y-\)min (lower - bound of the range) to a value less than or equal to \(9.3\) (e.g., \(y-\text{min}=0\)) and \(y-\)max (upper - bound of the range) to a value greater than or equal to \(34.1\) (e.g., \(y - \text{max}=40\)).

For part 2, when you make the scatter - plot (assuming a general form of a square - root - like relationship \(s = k\sqrt{d}\), since \(\sqrt{9}=3\), \(k=\frac{9.3}{3}=3.1\); \(\sqrt{25} = 5\), \(k=\frac{15.5}{5}=3.1\) etc., \(s = 3.1\sqrt{d}\)), there is no horizontal or vertical shift. A horizontal shift would be of the form \(y = a\sqrt{x - h}+k\) (\(h
eq0\)) and a vertical shift would be of the form \(y=a\sqrt{x}+k\) (\(k
eq0\)). In the relationship \(s = 3.1\sqrt{d}\) (or \(y = 3.1\sqrt{x}\) in the \(x - y\) coordinate system), \(h = 0\) and \(k = 0\).

Answer:

1. For the domain: set \(x-\text{min}\leq9\) (e.g., \(x-\text{min}=0\)) and \(x-\text{max}\geq121\) (e.g., \(x - \text{max}=150\)). For the range: set \(y-\text{min}\leq9.3\) (e.g., \(y-\text{min}=0\)) and \(y-\text{max}\geq34.1\) (e.g., \(y - \text{max}=40\)).
2. The graph does not show a horizontal or vertical shift.