The population P (in thousands) of San Jose, California,...

The population $P$ (in thousands) of San Jose, California, from 1980 to 2010 is shown in the table. (Midyear estimates are given.) Draw a rough graph of $P$ as a function of time $t.$ $$\begin{array}{|c|c|c|c|c|c|c|c|} \hline t & 1980 & 1985 & 1990 & 1995 & 2000 & 2005 & 2010 \\ \hline P & 629 & 714 & 782 & 825 & 895 & 901 & 946 \\ \hline \end{array}$$

The population $P$ (in thousands) of San Jose, California, from 1980 to 2010 is shown in the table. (Midyear estimates are given.) Draw a rough graph of $P$ as a function of time $t.$
$$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline t & 1980 & 1985 & 1990 & 1995 & 2000 & 2005 & 2010 \\
\hline P & 629 & 714 & 782 & 825 & 895 & 901 & 946 \\
\hline
\end{array}$$

Key Concepts

Scaling and Labeling Axes

Choosing appropriate scales and correctly labeling each axis ensures that the graphical representation accurately reflects the data. This process involves determining the range of values for both variables and marking intervals on the axes.

Plotting Data Points

Graphing involves marking points on the coordinate plane corresponding to pairs of values for the independent and dependent variables. When a chart of numerical values is given, each pair is plotted, and the overall trend can be observed upon connecting these points.

Graphing Functions

Drawing a rough graph of a function entails plotting the individual data points and then connecting them in a manner that illustrates the overall trend. This method helps in understanding the behavior of the function over the interval of interest.

Cartesian Coordinate System

A Cartesian coordinate system uses perpendicular axes to represent two variables graphically. In the context of plotting functions, one axis represents the independent variable while the other represents the dependent variable, enabling clear visualization of how one quantity changes in relation to another.

Independent and Dependent Variables

In function graphing, the independent variable is the input (often placed on the horizontal axis), and the dependent variable is the output (plotted on the vertical axis). Recognizing these roles is essential to correctly setting up and interpreting the graph.

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