Explaining if the tangent function is a continuous function or not

The video tutorial revisits the concept of tangent and its asymptotes, using the unit circle as a reference. It explains how tangent is defined as y/X and identifies angles where asymptotes occur. The instructor sketches the tangent graph, highlighting the asymptotes and discussing the function's continuity within specific intervals. Practical tips are provided for understanding graphs, emphasizing the importance of visualizing them without relying solely on calculators.

What is the definition of tangent in terms of the unit circle?

• y / x

• y - x

• x / y

• x + y

At which angle does the tangent function have an asymptote?

• π/2

• π

• 2π

• π/4

How do asymptotes affect the graph of the tangent function?

• They have no effect on the graph.

• They make the graph linear.

• They make the graph continuous.

• They create breaks in the graph.

Is the tangent function continuous over its entire domain?

• Yes, it is continuous everywhere.

• Yes, except at π.

• No, it is continuous only at π/2.

• No, it is not continuous due to asymptotes.

How does the continuity of the tangent function compare to that of the logarithm function?

• Neither function is continuous.

• Logarithm is continuous, but tangent is not.

• Tangent is continuous, but logarithm is not.

• Both are continuous over their entire domains.