Determine the solution by graphing the inequalities....

Key Concepts

Graphical Method for Solving Inequalities

Graphing inequalities provides a visual representation of the solution set by plotting the function and identifying regions where it satisfies the inequality. This technique helps in confirming the intervals obtained through algebraic methods and in understanding the behavior of the function across its domain.

Rational Inequalities

Rational inequalities involve expressions that consist of a ratio of polynomials. Solving these inequalities typically requires determining the sign of the rational expression in different intervals, taking into account the zeros of the numerator and the undefined points from the denominator.

Domain of Rational Functions

The domain of a rational function is the set of all values of the variable for which the function is defined. This usually involves excluding values that make the denominator zero. Understanding the domain is crucial in solving inequalities because it restricts the values under consideration.

Sign Analysis of Rational Expressions

Sign analysis is used to determine the intervals over which a rational expression is positive, negative, or zero. This involves checking the sign of the numerator and the denominator separately and then combining them. When the denominator is always positive, the sign of the rational expression is determined solely by the numerator.

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