Cosecant and Secant Function Concepts

The video tutorial covers graphing secant and cosecant functions. It begins with an introduction to these functions and explains how to graph them using their reciprocal functions, sine and cosine, as guidelines. The tutorial details the process of identifying vertical asymptotes and plotting minimum and maximum values to form parabolas. It also discusses transformations and provides practice problems to reinforce learning. The video emphasizes understanding the domain and range of these functions.

What is the first step in graphing the cosecant function?

• Graph the tangent function

• Graph the cosine function

• Graph the sine function

• Graph the cotangent function

Why do vertical asymptotes occur in the cosecant graph?

• Because sine is undefined at its maximum points

• Because sine is zero at its x-intercepts

• Because sine is undefined at its minimum points

• Because sine is zero at its maximum points

What do the minimum and maximum values of the sine function represent in the cosecant graph?

• The x-intercepts of the cosecant graph

• The vertical asymptotes of the cosecant graph

• The vertices of the parabolas in the cosecant graph

• The midline of the cosecant graph

What is the domain of the cosecant function?

• All real numbers except multiples of 2pi

• All real numbers except multiples of pi

• All real numbers except multiples of 3pi

• All real numbers except multiples of pi/2

Which function is used as a guideline for graphing the secant function?

• Cosine function

• Sine function

• Tangent function

• Cotangent function

Why do vertical asymptotes occur in the secant graph?

• Because cosine is undefined at its maximum points

• Because cosine is zero at its maximum points

• Because cosine is zero at its x-intercepts

• Because cosine is undefined at its minimum points

What is the period of the parent function of secant?

• pi

• 3pi

• pi/2

• 2pi

How does a vertical stretch affect the graph of secant?

• It changes the period

• It changes the amplitude

• It changes the vertical asymptotes

• It changes the phase shift

What is the range of the transformed cosecant function with an amplitude of 2?

• y ≥ 3 and y ≤ -3

• y ≥ 0.5 and y ≤ -0.5

• y ≥ 1 and y ≤ -1

• y ≥ 2 and y ≤ -2