Question
Changes in Midline Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Question
Use the table to answer the question.
x 0 π2 π 3π2 2π
y −3 −2 −3 −4 −3
Review the table of values to determine the midline for the sine function.(1 point)
The equation of the midline is y=
.
Remaining Attempts : 3
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Answers
GPT-4o mini
To determine the midline of a sine function from a table of values, you need to find the average of the maximum and minimum values of \(y\).
From the table:
- The minimum \(y\) value is \(-4\) (at \(x = \frac{3\pi}{2}\)).
- The maximum \(y\) value is \(-2\) (at \(x = \frac{\pi}{2}\)).
Now, calculate the midline:
\[
\text{Midline} = \frac{\text{Maximum} + \text{Minimum}}{2} = \frac{-2 + (-4)}{2} = \frac{-6}{2} = -3
\]
Thus, the equation of the midline is:
\[
y = -3
\]
From the table:
- The minimum \(y\) value is \(-4\) (at \(x = \frac{3\pi}{2}\)).
- The maximum \(y\) value is \(-2\) (at \(x = \frac{\pi}{2}\)).
Now, calculate the midline:
\[
\text{Midline} = \frac{\text{Maximum} + \text{Minimum}}{2} = \frac{-2 + (-4)}{2} = \frac{-6}{2} = -3
\]
Thus, the equation of the midline is:
\[
y = -3
\]