Question

drag and drop the features of the trigonometric functions to the graph of the function

drag & drop the answer

midline = -1
midline = -2
midline = -3
midline = -4
amplitude = 1
amplitude = 2
amplitude = -3
amplitude = 4
period = 2\pi
period = \pi/2
period = \pi
period = 2\pi/3

row 1
column 2

Explanation:

⚡ Using what you learned: Graphing Trigonometric Functions

Step 1: Analyze the first graph (Row 1)

• Orientation: Note that the image is rotated \(90^\circ\) counterclockwise. Looking at the graph labeled "ROW 1" (the top graph when rotated correctly):
• The horizontal axis (independent variable, usually \(x\)) has grid markings.
• The vertical axis (dependent variable, usually \(y\)) has values. Let's find the maximum and minimum values of the wave:
• Maximum value: \(y = 1\)
• Minimum value: \(y = -3\)
• Midline: The horizontal line halfway between the maximum and minimum:

\[
\text{Midline} = \frac{\text{Maximum} + \text{Minimum}}{2} = \frac{1 + (-3)}{2} = -1
\]
So, the midline is \(y = -1\).

• Amplitude: The vertical distance from the midline to a peak or trough:

\[
\text{Amplitude} = \text{Maximum} - \text{Midline} = 1 - (-1) = 2
\]

• Period: The horizontal distance for one complete cycle:
• A peak occurs at \(x = 0\).
• The next peak occurs at \(x = 2\pi\).
• Therefore, the period is \(2\pi\).

Step 2: Analyze the second graph (Column 2)

• Looking at the graph labeled "COLUMN 2" (the bottom graph when rotated correctly):
• Maximum value: \(y = 1\)
• Minimum value: \(y = -7\)
• Midline:

\[
\text{Midline} = \frac{1 + (-7)}{2} = -3
\]
So, the midline is \(y = -3\).

• Amplitude:

\[
\text{Amplitude} = 1 - (-3) = 4
\]

• Period:
• A peak occurs at \(x = 0\).
• The next peak occurs at \(x = \frac{2\pi}{3}\).
• Therefore, the period is \(\frac{2\pi}{3}\).

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Answer:

ROW 1 (Top Graph):

• Midline: midline = -1
• Amplitude: Amplitude = 2
• Period: Period = \(2\pi\)

COLUMN 2 (Bottom Graph):

• Midline: midline = -3
• Amplitude: Amplitude = 4
• Period: Period = \(2\pi/3\)