Graphs of Functions

Preliminary Activity. Consider the data presented in Table 3.7 on the number of homicides in the city of New York for the years 1985 through 1996. Study the data and find a way to present them visually so that the trends in the homicide rate are easily seen. Based on this visual presentation, explain, as best you can, the trends found in the data. 

NYSE Volume (in Millions) from March 21-June 9, 1998 

Date Volume Date Volume Date Volume Dale Volume 

Ignoring holidays and weekends (when trading = 0), when was the most dramatic increase and decrease in the volume of shares traded  

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Here cr(—1) moves points on R one unit to the left and /)(— ) moves graphs one unit to the left. More generally, if [Pg.130]

Experimental data and graphs of function (25) (inverted coordinates) describing growth of yeast in the presence of chromium and nickel salts are presented in Figure 2 [14]. In the limits of measurements accuracy the calculated curves are in good agreement with experimental data under change of number approximately by six orders. 

A term expressing correlation. In graphs of functional relationships between two variables, changes in one variable (for example, drug effect) associated with changes in another (drug dose) are represented. 

Now it is possible to construct, 10 points of the graph of function x = straight line segments obtain a broken line, which is the first approximation to the curve x = [Pg.109]

Graphs of functions b m) and b g m) are given in Fig. 9.2. With an increase of the distance from the source and conductivity of a medium, due to transformation of the electromagnetic energy into heat, the field magnitude, corresponding to the moment of the first arrival, rapidly decreases. 

Table 9.2 contains values of function hn, hg and depending on parameter u. Graphs of functions hfi, hg and e, provided that the dipole current is turned on at the moment t = 0, are given in Fig. 9.5. For this reason, with an increase of time the magnetic field tends to that of the direct current while the electric field vanishes, i.e. as... 

Graphs of function are presented in Fig. 9.6. With an increase of time... 

Graphs of functions involve one dependent variable and one or two independent variables. For example, the function y = x is shown in Figure 2.1. The two or three variables involved can be said to define a Variable Space, within which the function forms a line or a surface. Functions with more than three variables cannot, of course, be represented in three dimensional space, but can still be thought of as surfaces in a higher-order space or hyperspace. 

Let us consider the graph of function f x) = A e where A is some constant. Depending on the value of A, the curve would be a tangent at f x) = 1 x = 1 passing through the origin as shown below. 

These functions are called circular or trigonometric functions. Note that Equations (2-25) are just the transformation Equations (1-4) with r = 1. It is interesting to compare the graphs of functions, such as sin 0 and cos 0, in linear coordinates (coordinates in which 0 is plotted along one axis) to those in plane polar coordinates. Consider, for example, the equation r = A cos 0y where A is a constant. Such an equation can be used to describe the wave properties of p-type atomic orbitals in two dimensions. The functional dependence of r upon 0 can be seen in Table 2-1. 

It can be seen that the oscillation of kinetic and potential energies accomplishes with the doubled frequency 2oj in comparison with the initial one. Graphs of functions (t), K(f) and U t) are presented in the Figure 2.12. 

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