Math Clip Art--Function Concepts--Graphs of Functions and Relations--Tangent Curve

Topic

Functions

Description

This clip art depicts the graph of the tangent function, a key trigonometric function. The tangent function is periodic but unlike sine or cosine, it has discontinuities. It passes the vertical line test and is thus a function, albeit one with unique characteristics.

The tangent curve is distinguished by its vertical asymptotes, occurring at regular intervals where the function approaches infinity. These asymptotes correspond to angles where cosine equals zero. The function's behavior between these asymptotes, alternating between positive and negative infinity, makes it a powerful tool for modeling certain physical phenomena.

Visualizing the tangent function helps students understand concepts like periodicity, asymptotes, and the relationship between trigonometric functions. It's an excellent example of how a function can be both continuous and discontinuous in different parts of its domain.

Teacher's Script: "Look at this interesting curve. Can you spot the places where it seems to shoot up or down infinitely? These are called asymptotes. How does this graph differ from sine or cosine? Let's discuss why these 'breaks' in the curve occur and what they mean mathematically."

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