Understanding Secant Function Transformations

The video tutorial explains how to describe and graph the transformation of the function y = 3 sec(pi x + pi/2) + 1. It covers the transformation in terms of amplitude, period, phase shift, and vertical shift. The tutorial emphasizes that secant functions do not have an amplitude like sine and cosine functions. It then demonstrates graphing the corresponding cosine function to aid in sketching the secant function, highlighting the relationship between the two functions, including vertical asymptotes and concavity.

What is the general form of the secant function transformation?

• y = a * cos(bx + c) + d

• y = a * sin(bx + c) + d

• y = a * sec(bx + c) + d

• y = a * tan(bx + c) + d

Which parameter affects the vertical shift of the secant function?

• d

• c

• b

• a

How is the period of the secant function determined?

• 2π divided by a

• 2π divided by b

• 2π divided by c

• 2π divided by d

What is the phase shift of the function y = 3 sec(πx + π/2) + 1?

• Left 1 unit

• Right 1/2 unit

• Left 1/2 unit

• Right 1 unit

Why is it useful to graph the corresponding cosine function first?

• Cosine and secant have the same period

• Cosine and secant have reciprocal values

• Cosine and secant have the same phase shift

• Cosine and secant have the same amplitude

What is the amplitude of the cosine function y = 3 cos(πx + π/2) + 1?

• 1

• 2

• 4

• 3

Where does the cosine function start when graphing one period?

• At the minimum

• At the origin

• At the maximum

• At the midline

What is the significance of vertical asymptotes in the secant graph?

• They occur where the cosine function is maximum

• They occur where the cosine function is zero

• They indicate minimum points

• They indicate maximum points

How does the secant function behave where the cosine function is concave down?

• Secant is concave down

• Secant is concave up

• Secant is linear

• Secant is constant

What is the relationship between the max/min points of cosine and secant functions?

• They are unrelated

• They are shifted by π/2

• They are the same points

• They are opposite points