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In the graph you've provided, the solution to the inequality \(f(x) < g(x)\) can be determined by identifying the range of \(x\) values for which the blue quadratic curve \(f(x)\) is below the red linear curve \(g(x)\).

From the graph, it is clear that the quadratic function \(f(x)\) intersects the linear function \(g(x)\) at two points. These points appear to be \(x = -1\) and \(x = 2\). Between these two points, the graph of \(f(x)\) is below that of \(g(x)\).

Therefore, the solution to the inequality \(f(x) < g(x)\) is the interval:
\[
x \in (-1, 2)
\]
This indicates that for every \(x\) value between -1 and 2 (not including -1 and 2 themselves), the quadratic function \(f(x)\) will have a lower value than the linear function \(g(x)\).

Would you like more details on this or have any other questions? Here are some related topics to explore:

1. How would you solve this algebraically if the equations of \(f(x)\) and \(g(x)\) were given?
2. What does the solution mean graphically in terms of the areas under each curve?
3. What are the vertex and axis of symmetry for the quadratic function based on the graph?
4. How do changes in the coefficients of the linear equation affect the intersection points with the quadratic curve?
5. How can you verify the solution interval \( (-1, 2) \) using a table of values for \(f(x)\) and \(g(x)\)?

**Tip**: To understand how the coefficients of a quadratic equation affect its graph, explore variations in the values of \(a\), \(b\), and \(c\) in the standard form \(ax^2 + bx + c\), and observe changes in the parabola's shape, position, and orientation.

Solve the inequality f(x) < g(x) using the graph of a quadratic function f(x) and a linear function g(x).

Learn how to solve the inequality f(x) < g(x) by analyzing the intersection points between a quadratic function and a linear function graphically. Explore key concepts such as quadratic and linear functions, graphical solutions, and inequalities. Suitable for students in Grades 9-11.

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