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Changes in Midline Practice
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A waveform is plotted on a coordinate plane. The x-axis ranges from negative 2 pi to 2 pi in increments of start fraction pi over 2 end fraction. The y-axis ranges from negative 1 to 3 in unit increments.
What is the value of d in the function f(x)=sin(x)+d
in the function shown in the graph?
(1 point)
The value of d in the function f(x)=sin(x)+d
is
.
Remaining Attempts : 3
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Answers
GPT-4o mini
To determine the value of \( d \) in the function \( f(x) = \sin(x) + d \), we need to find the vertical shift of the sine wave represented in the graph.
The sine function \( \sin(x) \) oscillates between -1 and 1. The graph of \( f(x) = \sin(x) + d \) will shift the entire sine wave vertically by \( d \).
1. **Identify the maximum and minimum values of the function on the graph**:
- The standard sine function \( \sin(x) \) reaches a maximum of 1 and a minimum of -1.
- Thus, the new maximum will be \( 1 + d \) and the new minimum will be \( -1 + d \).
2. **Using the y-axis range from the graph**:
- According to your description, the y-axis ranges from -1 to 3.
- This means that the maximum value (top of the curve) is 3.
- Thus, we can equate this to the maximum value of the shifted sine function:
\[
1 + d = 3
\]
- Solving for \( d \):
\[
d = 3 - 1 = 2
\]
3. **Final answer**:
- The value of \( d \) in the function \( f(x) = \sin(x) + d \) is \( 2 \).
The sine function \( \sin(x) \) oscillates between -1 and 1. The graph of \( f(x) = \sin(x) + d \) will shift the entire sine wave vertically by \( d \).
1. **Identify the maximum and minimum values of the function on the graph**:
- The standard sine function \( \sin(x) \) reaches a maximum of 1 and a minimum of -1.
- Thus, the new maximum will be \( 1 + d \) and the new minimum will be \( -1 + d \).
2. **Using the y-axis range from the graph**:
- According to your description, the y-axis ranges from -1 to 3.
- This means that the maximum value (top of the curve) is 3.
- Thus, we can equate this to the maximum value of the shifted sine function:
\[
1 + d = 3
\]
- Solving for \( d \):
\[
d = 3 - 1 = 2
\]
3. **Final answer**:
- The value of \( d \) in the function \( f(x) = \sin(x) + d \) is \( 2 \).