Math Clip Art--Function Concepts--Function Graphs 08

Topic

Functions

Description

This image illustrates a circular graph with points plotted on a grid. Red dashed vertical lines are drawn through the circle, clearly demonstrating that it fails the vertical line test by intersecting multiple points vertically. This visual representation serves as an excellent example of a graph that does not represent a function.

The circular shape of the graph is particularly effective in showcasing why certain relations cannot be classified as functions. By observing how the vertical lines intersect the circle at more than one point, students can easily grasp the concept that for a relation to be a function, each input value must correspond to exactly one output value.

Using this type of visual aid allows educators to emphasize the critical distinction between functions and non-functions. It provides an opportunity to discuss the importance of the vertical line test in determining whether a graph represents a function. This image can also serve as a springboard for more advanced topics, such as how portions of the circle could be considered functions if the domain is restricted.

Teacher's Script: "Let's examine this circular graph. Notice the red dashed vertical lines - what do you observe about where they intersect the circle? Why does this mean the graph doesn't represent a function? Can you think of any real-world scenarios that might be represented by a circular graph like this? How might we modify this graph to make it represent a function?"

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