To graph the function \( y = -2\sqrt{x} + 1 - 3 \), we will first simplify the function:
\[ y = -2\sqrt{x} - 2 \]
Now, we can calculate the corresponding \( y \) values for the provided \( x \) values (-1, 0, 3).
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For \( x = -1 \): The square root of a negative number is not defined in the set of real numbers. Therefore, there is no value for \( y \) when \( x = -1 \).
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For \( x = 0 \): \[ y = -2\sqrt{0} - 2 = -2 \cdot 0 - 2 = -2 \]
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For \( x = 3 \): \[ y = -2\sqrt{3} - 2 \approx -2(1.732) - 2 \approx -3.464 - 2 \approx -5.464 \]
Now we can summarize the points:
- For \( x = -1 \), \( y \) is not defined.
- For \( x = 0 \), \( y = -2 \).
- For \( x = 3 \), \( y \approx -5.464 \).
Therefore, the completed table is:
| \( x \) | \( y \) | |---------|---------------| | -1 | Not Defined | | 0 | -2 | | 3 | -5.464 |