Solving Rational Inequalities Using a Graph | Precalculus

Identifying When g(x) < 0

• 🎯 The goal is to find the intervals where the function g(x) is less than zero, based on its provided graph.
• ⚠️ It's crucial to note that the inequality is strictly 'less than zero', not 'less than or equal to zero'.

Analyzing the Graph

• 📉 The graph visually shows where the function's y-values are negative.
• 🔍 The highlighted sections of the graph indicate where g(x) is less than 0.

Key Intervals and Vertical Asymptotes

• ⚠️ Vertical asymptotes are present at x = -3 and x = 3, meaning the function is undefined at these points.
• ➡️ One interval where g(x) < 0 is between x = -3 and x = -2, expressed as -3 < x < -2.
• ➡️ Another interval where g(x) < 0 is between x = 2 and x = 3, expressed as 2 < x < 3.

Interval Notation

• 🔗 The solution can be represented using interval notation as the union of two open intervals: (-3, -2) U (2, 3).
• 💡 This notation signifies that the solution includes all values of x strictly between -3 and -2, and strictly between 2 and 3.