Making Sense of Mathematics for Teaching High School by Nolan Edward C.;Dixon Juli K.;Safi Farshid;Haciomeroglu Erhan Selcuk;

Author:Nolan, Edward C.;Dixon, Juli K.;Safi, Farshid;Haciomeroglu, Erhan Selcuk;
Language: eng
Format: epub
Publisher: Solution Tree
Published: 2016-08-15T00:00:00+00:00

What conclusions can you draw from the values listed in table 4.1? What do you notice about the values chosen for x? How do you make the connections between the values of x, the function values, and their meaning for the population growth over time? The outputs from the four given functions are all equal in the second row of table values—namely when x equals 2, which happens to be a commonly selected value to test in order to determine which function is greater. Would the values in table 4.1 represent sufficient information to determine which function describes the greater population growth? Notice how the answer to that question depends on the values of x that you chose to examine. You need to think about what knowledge and strategies are needed to recognize whether the values in table 4.1 represent sufficient information to determine which function has the greatest growth in function values.

Note how some of the values for x negate the idea that the linear function with the greater slope (f(x) = 2x) consistently produces greater function values than the linear function with the lesser slope (g(x) = x + 2). A quick look at the graph of these two linear functions may also provide insight in distinguishing between function values and slope (see figure 4.2).

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