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

Tags

CCSS.HSF-IF.C.7E

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

Tags

CCSS.HSF.TF.A.4

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

• PI/4 radians

• PI/2 radians

• 2PI radians

• 4PI radians

Tags

CCSS.HSF-IF.C.7E

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

Tags

CCSS.HSF-IF.C.7E

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

• Y = 1

• Y = 4

• Y = -1

• Y = 0

Tags

CCSS.HSF-IF.C.7E

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

• 1.5

• 1.7

• 1.4

• 1.6

Tags

CCSS.HSF-IF.C.7E

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

Tags

CCSS.HSF.TF.A.4

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

• 3

• 4

• 5

• 6

Tags

CCSS.HSF.TF.A.4

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

• -4

• -6

• -3

• -5

Tags

CCSS.HSF-IF.C.7E

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

Tags

CCSS.HSF-IF.C.7E