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

Topic

Functions

Description

This clip art depicts a rational function graph. Rational functions are quotients of polynomials and can have a wide variety of shapes depending on the degrees of the numerator and denominator. They generally pass the vertical line test and are thus functions, though they may have discontinuities.

Rational functions are important in advanced algebra and calculus. They exhibit interesting behaviors like vertical and horizontal asymptotes, holes, and intercepts. These functions are used to model complex relationships in physics, engineering, and economics.

Visualizing rational functions helps students understand concepts like domain restrictions, asymptotic behavior, and the effects of factors in the numerator and denominator. This graph can be used to discuss limits, continuity, and the behavior of functions near their asymptotes.

Teacher's Script: "Observe the different parts of this graph. Can you identify any asymptotes or holes? Let's discuss how the degrees of the numerator and denominator affect the graph's shape. How might we use rational functions to model real-world scenarios?"

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