By Denes Petz
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Extra resources for An Invitation to the Algebra of Canonical Commutation Relations
From the data we see that for each 1-km increase in elevation, the temperature decreases by 10°C. So at an elevation of h km we must subtract 10h degrees from the ground temperature. ✓ C H E C K To check that this equation correctly models the data, we try some values for h from the table. 2 Model T = 20 - 10152 Replace h by 5 T = - 30 Calculate This matches the temperature given in the table for an elevation of 5 km. You can check that the other values in the table also satisfy this equation. (c) We plot the points in the table and then complete the graph by drawing the line that contains the plotted points.
B) List the ordered pair(s) whose input is 50 and the ordered pair(s) with input 72. (c) Use the Vertical Line Test to determine whether the relation is a function. y 10 Times per 8 month at 6 restaurant 4 2 0 20 30 40 50 Age 60 70 80 x 52 CHAPTER 1 ■ Data, Functions, and Models 65. Algebra and Alcohol The first two columns of the table in the Prologue (page P2) give the alcohol concentration at different times following the consumption of 15 mL of alcohol. (a) Do these data define the alcohol concentration as a function of time?
If we call this rule g, then we can write this function as g1x2 = x 2 + 2x (b) If we write y for the output f 1x 2 , then we can write the function as y = 5x + 1 The dependent variable is y, and the independent variable is x. ■ 2 NOW TRY EXERCISES 23 AND 29 ■ ■ Evaluating Functions—Net Change In function notation the input x plays the role of a placeholder.
An Invitation to the Algebra of Canonical Commutation Relations by Denes Petz