To graph the function \( y = \sin(x) + 23 \), we start by understanding the transformation applied to the sine function.
The function \( \sin(x) \) oscillates between -1 and 1. Therefore, when we add 23 to the sine function, the entire graph is shifted upward by 23 units. As a result, the new range of the function \( y = \sin(x) + 23 \) will be between 22 and 24:
- Minimum value: \( -1 + 23 = 22 \)
- Maximum value: \( 1 + 23 = 24 \)
Now, let’s analyze the provided tables of values to find one that represents this transformation:
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In the first option:
- \( y = -23, 13, -23, -53, -23 \) (does not match our range)
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In the second option:
- \( y = -\frac{2}{3}, \frac{1}{3}, -\frac{2}{3}, -\frac{5}{3}, -\frac{2}{3} \) (does not match our range)
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In the third option:
- \( y = 23, 53, 23, -13, 23 \) (includes 23, not within the correct range)
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In the fourth option:
- \( y = \frac{5}{3}, \frac{2}{3}, -\frac{1}{3}, \frac{2}{3}, \frac{5}{3} \) (does not match our range)
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In the fifth option:
- \( y = 53, 23, -13, 23, 53 \) (includes values above 24 and below 22)
The correct values for \( y = \sin(x) + 23 \) should range from 22 to 24.
Conclusion: None of the given tables are correct to graph \( y = \sin(x) + 23 \) since none fit the expected range of values. If one of the options had values of \( y \) that were strictly between 22 and 24, that would be the appropriate one, but there appear to be no such options listed.
1 answer