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Chapter 2: Problem 83

If \(f\) is a polynomial or rational function, explain how the graph of \(f\) can be used to visualize the solution set of the inequality \(f(x)<0\).

Short Answer

Expert verified
The solution set of the inequality \( f(x) < 0 \) can be visualized on a graph by identifying the intervals where the curve of the function \( f(x) \) is below the x-axis.

Step by step solution

01

Understanding the graph

When we graph a function, each point \( (x, f(x)) \) on the graph represents the function value at that point. When \( f(x) < 0 \), it means that the value of the function at point x is less than zero. In terms of the graph, this means the graph of the function is below the x-axis
02

Identifying the intervals

To identify when \( f(x) < 0 \), we look for the intervals on the x-axis where the function curve is below the x-axis.
03

Visualize the Solution on Graph

The values of x for which the graph of \( f(x) \) dips below the x-axis provide the solution set for \( f(x) < 0 \). Therefore, the graph visualization helps easily identify the solution set of the inequality \( f(x) < 0 \).

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