Unformatted text preview: . Continuing, we see that on (1, ∞), the graph
of y = h(x) is above the x-axis, and so we mark (+) there. To construct a sign diagram from this
information, we not only need to denote the zero of h, but also the places not in the domain of
h. As is our custom, we write ‘0’ above 2 on the sign diagram to remind us that it is a zero of h.
We need a diﬀerent notation for −1 and 1, and we have chosen to use ‘ ’ - a nonstandard symbol
called the interrobang. We use this symbol to convey a sense of surprise, caution, and wonderment
- an appropriate attitude to take when approaching these points. The moral of the story is that
when constructing sign diagrams for rational functions, we include the zeros as well as the values
excluded from the domain.
Steps for Constructing a Sign Diagram for a Rational Function
Suppose r is a rational function.
1. Place any values excluded from the domain of r on the number line with an ‘ ’ above them.
2. Find the zeros of r and place them on the number line with the number 0 above them.
3. Choose a test value in each of the intervals determined in steps 1 and 2.
4. Determine the sign of r(x) for each test value in step 3, and write that sign above the
We now present our procedure for graphing rational functions and apply it to a few exhaustive
examples. Please note that we decrease the amount of detail given in the explanations as we move
through the examples. The reader should be ab...
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