Line Intersecting a Cubic Function

This example demonstrates how a straight line intersects the graph of a cubic function, with the number of intersection points changing dynamically as the line's position varies. The core mathematical concepts include the shape of cubic functions, solving intersections between a line and a curve, and the relationship between intersection points and roots of equations. The construction uses GeoGebra objects a, b, d, c, f, m, k, and g, where f represents the cubic function and g the line, with sliders or parameters controlling the slope m and intercept k to observe changes in intersection count (1, 2, or 3 points). It is suitable for high school students learning functions and equations, as well as for pre-calculus or introductory calculus demonstrations of line-curve interactions.