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Let us start by looking at the definition in the textbook (and also in the Chapter Summary)
Graph of a Function
The graph of the function f is the set of all points (x, f(x)) in the xy-plane, where we restrict the values of x to lie in the domain of f.
To obtain the graph of a function, plot points of the form (x, f(x)) for several values of x in the domain of f. The shape of the entire graph can usually be inferred from sufficiently many points.
To sketch the graph of the function
If only the graph of a function is given to begin with, we say that the function has been specified graphically. Here is an example of a graphically specified function.
The following graph shows the total population in state and federal prisons in 1970-1997 as a function of time in years (t = 0 represents 1970).*
Here is what we get if we carefully plot the points we just obtained.
Since piecewise-defined functions are based on more than one-formula, their graphs are composed of more than one curve. Here is Example 4 in the textbook: Let
The graph of f consists of portions of three graphs superimposed. To see how they fit together, click the buttons under the graph of f below.
Now try some of the exercises in Section 1.2 of the textbook, or press "Review Exercises" on the sidebar to see a collection of exercises that covers the whole of Chapter 1.