Math Clip Art--Function Concepts--Graphs of Functions and Relations--Cubic Function Graph

Topic

Functions

Description

This clip art showcases the graph of a cubic function, a polynomial function of degree three. Cubic functions always pass the vertical line test, confirming their status as functions. The graph typically has a characteristic S-shape, with one or three real roots.

Cubic functions are significant in algebra as they represent the next level of complexity after quadratic functions. They can model a wide range of phenomena, from the volume of a box to the motion of a pendulum. The shape of a cubic function graph can vary significantly based on its coefficients, potentially including points of inflection and local extrema.

Visualizing cubic functions helps students understand concepts like roots, turning points, and end behavior of polynomial functions. It's an excellent tool for introducing more advanced topics in algebra and calculus, such as optimization problems and curve sketching.

Teacher's Script: "Look at this S-shaped curve. Can you identify where it crosses the x-axis? These points are called roots. How many turning points do you see? Let's discuss how changing the coefficients in a cubic equation might affect the shape of this graph. Can you think of any real-world scenarios that might be modeled by a cubic function?"

For a complete collection of math clip art related to Functions and Relations click on this link: Graphs of Functions and Relations Collection.