Question

To graph the square root function y=-2 square root x+1-3, complete the table of data points for the function. x=-1,0,3; y= ?,?,?

Answer 1

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).

1. **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 \( x = -1 \).

2. **For \( x = 0 \)**:
\[
y = -2\sqrt{0} - 2 = -2 \cdot 0 - 2 = -2
\]

3. **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 |