Question

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

row 1

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

column 2

Explanation:

⚡ Using what you learned: Graphing Trigonometric Functions

Step 1: Analyze the graph in ROW 1 (Left Graph)

• Midline: The horizontal line that runs halfway between the maximum and minimum values.
• Maximum value: \(y = 3\)
• Minimum value: \(y = -5\)
• Midline calculation:

\[
y = \frac{3 + (-5)}{2} = -1
\]

• Therefore, Midline = -1.

• Amplitude: The vertical distance between the midline and a peak (or trough).
• Amplitude calculation:

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

• Therefore, Amplitude = 4.

• Period: The horizontal distance required for the function to complete one full cycle.
• Looking at the x-axis, a full cycle starts at \(x = 0\) (on the midline, going up) and completes its next upward-going midline crossing at \(x = \pi\).
• Therefore, Period = \(\pi\).

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Step 2: Analyze the graph in COLUMN 2 (Right Graph)

• Midline:
• Maximum value: \(y = -1\)
• Minimum value: \(y = -5\)
• Midline calculation:

\[
y = \frac{-1 + (-5)}{2} = -3
\]

• Therefore, Midline = -3.

• Amplitude:
• Amplitude calculation:

\[
\text{Amplitude} = -1 - (-3) = 2
\]

• Therefore, Amplitude = 2.

• Period:
• Looking at the x-axis, the distance between consecutive peaks is from \(x = 0\) to \(x = \frac{2\pi}{3}\).
• Therefore, Period = \(2\pi/3\).

Answer:

• ROW 1 (Left Graph Features):
• Midline = -1
• Amplitude = 4
• Period = \(\pi\)

• COLUMN 2 (Right Graph Features):
• Midline = -3
• Amplitude = 2
• Period = \(2\pi/3\)