Math Clip Art--Function Concepts--Function Graphs 03

Topic

Functions

Description

This image showcases a graph with points labeled (a, b), (c, d), (e, f), and (g, h) connected by line segments. It demonstrates that a function can be graphed as a set of x-y coordinates with the segments connecting them, illustrating a step towards continuous function representation.

The connected points in this graph build upon the previous concept of discrete coordinates, introducing the idea of interpolation between known data points. This visualization helps students understand how functions can be represented as continuous lines or curves, even when only specific points are known. It's an excellent tool for discussing linear functions, piecewise functions, and the concept of continuity.

By using this visual representation, educators can guide students in exploring the relationship between discrete data points and continuous function graphs. This image provides an opportunity to discuss concepts such as slope, rate of change, and linear interpolation. It also serves as a bridge between the discrete representation of functions and more complex, continuous function graphs.

Teacher's Script: "Now we see the same points as before, but this time they're connected by line segments. How does this change our understanding of the function? What can we infer about the function's behavior between the given points? Let's discuss how this representation differs from the previous one and what additional information it provides about the function."

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