Understanding Trigonometric Transformations

The video tutorial explains how to describe and graph a trigonometric transformation of the function Y = 4 x COSINE (4X - 8) - 1. It covers factoring the equation to fit the standard form, identifying parameters A, B, C, and D, and describing the amplitude, period, phase shift, and midline. The tutorial then guides through the process of graphing the function, considering the phase shift and period, and dividing the interval into equal parts to accurately plot the cosine function over one period.

What is the first step in transforming the equation Y = 4 x COSINE (4X - 8) - 1?

• Identify the amplitude

• Factor the expression inside the cosine

• Calculate the period

• Determine the phase shift

How is the amplitude of the function Y = 4 x COSINE (4X - 8) - 1 determined?

• By adding D to C

• By subtracting C from D

• By taking the absolute value of A

• By dividing 2PI by B

What is the period of the function Y = 4 x COSINE (4X - 8) - 1?

• PI/4 radians

• PI/2 radians

• 2PI radians

• 4PI radians

In which direction is the phase shift for the function Y = 4 x COSINE (4X - 8) - 1?

• 2 units to the left

• 2 units to the right

• 4 units to the right

• 4 units to the left

What is the new midline of the function Y = 4 x COSINE (4X - 8) - 1?

• Y = 1

• Y = 4

• Y = -1

• Y = 0

What is the approximate value of PI/2 used for graphing?

• 1.5

• 1.7

• 1.4

• 1.6

Where does the graph of the function start after considering the phase shift?

• At 3 units

• At 1 unit

• At 0 units

• At 2 units

What is the maximum value of the function Y = 4 x COSINE (4X - 8) - 1?

• 3

• 4

• 5

• 6

What is the minimum value of the function Y = 4 x COSINE (4X - 8) - 1?

• -4

• -6

• -3

• -5

How does the cosine function behave over one period?

• Starts at a maximum, then midline, minimum, midline

• Starts at midline, then minimum, midline, maximum

• Starts at a minimum, then midline, maximum, midline

• Starts at midline, then maximum, midline, minimum