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Unformatted text preview: for Constructing a Sign Diagram for an Algebraic Function
Suppose f is an algebraic function.
1. Place any values excluded from the domain of f on the number line with an ‘ ’ above them.
2. Find the zeros of f 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 f (x) for each test value in step 3, and write that sign above the
Our next example reviews quite a bit of Intermediate Algebra and demonstrates some of the new
features of these graphs.
Example 5.3.1. For the following functions, state their domains and create sign diagrams. Check
your answer graphically using your calculator.
1. f (x) = 3x 3 2 − x 2. g (x) = 2− √
4 x+3 3. h(x) = 3 4. k (x) = √ 8x
x2 − 1 Solution.
1. As far as domain is concerned, f (x) has no denominators and no even roots, which means its
domain is (−∞, ∞). To create the sign diagram, we ﬁnd the zeros of f .
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