# 3.4 The Graph of a Function

**Table of Values • Plotting Points • Be Careful about the Domain • Vertical-Line Test • Finding Domain and Range Graphically**

Now that we have introduced the concepts of a function and the rectangular coordinate system, we are in a position to determine the graph of a function. In this way, we will obtain a visual representation of a function.

The graph of a function is the set of all points whose coordinates (*x, y*) satisfy the functional relationship $y\hspace{0.17em}=\hspace{0.17em}f(x)\hspace{0.17em}.\hspace{0.17em}$ Because $y\hspace{0.17em}=\hspace{0.17em}f(x)\hspace{0.17em},\hspace{0.17em}$ we can write the coordinates of the points on the graph as (`x`, `f`(`x`)). Writing the coordinates in this manner tells us exactly how to find them. *We assume a certain value for x and then find the value of the function of x. These two numbers ...*

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