Tangent Function Properties and Behavior

This video tutorial explores the properties of tangent functions, including their domain, range, asymptotes, zeros, period, and symmetry. It explains how tangent functions differ from sine and cosine functions, particularly in having vertical asymptotes and a period of pi. The tutorial also covers how to graph a basic tangent function, highlighting its symmetry about the origin and the behavior of the function as it approaches its asymptotes.

What is the domain of the tangent function?

• All integers

• All real numbers except even multiples of pi

• All real numbers except odd multiples of pi/2

• All real numbers

What is the range of the tangent function?

• All real numbers

• From 0 to 1

• From -1 to 1

• From -infinity to 0

Where do vertical asymptotes occur in the tangent function?

• At multiples of 2pi

• At odd multiples of pi/2

• At multiples of pi

• At even multiples of pi/2

At which points does the tangent function have zeros?

• At odd multiples of pi/2

• At multiples of 2pi

• At even multiples of pi/2

• At multiples of pi

What is the period of the tangent function?

• 4pi

• pi/2

• pi

• 2pi

Why is the tangent function considered an odd function?

• Because it is symmetric about the y-axis

• Because it is symmetric about the x-axis

• Because it is symmetric about the origin

• Because it has no symmetry

Which of the following functions is an even function?

• Cosine

• Secant

• Sine

• Tangent

What happens to the tangent function as it approaches pi/2?

• It approaches zero

• It approaches infinity

• It remains constant

• It approaches negative infinity

How does the tangent function behave between its asymptotes?

• It increases and decreases without bound

• It oscillates between -1 and 1

• It remains constant

• It decreases to zero

What is the significance of the graph's symmetry in the tangent function?

• It shows the function is periodic

• It shows the function is even

• It shows the function is constant

• It shows the function is odd