Math Clip Art--Function Concepts--Function Graphs 07

Topic

Functions

Description

This image shows a graph with a diagonal line passing through several points on a grid. Red dashed vertical lines indicate that the line passes the vertical line test, providing another example of a function graph that satisfies this crucial criterion.

The diagonal line and the red dashed vertical lines reinforce the concept of the Vertical Line Test. This visualization helps students understand that linear functions always pass the Vertical Line Test, as any vertical line will intersect the diagonal line exactly once. It's an excellent tool for discussing the properties of linear functions in the context of the function definition.

Using this type of visual representation allows educators to emphasize the connection between the algebraic and graphical representations of functions. Students can see how the one-to-one correspondence between x and y values in a linear equation translates to a graph that passes the Vertical Line Test. This image provides an opportunity to discuss concepts such as domain and range, and how they relate to the Vertical Line Test. It also sets the stage for comparing linear functions with other types of functions that pass the Vertical Line Test.

Teacher's Script: "Here we see a diagonal line with red dashed vertical lines. What do these vertical lines tell us about this graph? How does this relate to our definition of a function? Let's discuss why linear functions always pass the Vertical Line Test and what this means for their behavior."

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