Question

To graph the square root function y=−2x+1−−−−−√−3 , complete the table of data points for the function.(3 points) Complete the table by finding the y-values. x y -1 0 3

Answer 1

To graph the function \( y = \sqrt{-2x + 1} - 3 \), we need to calculate the corresponding \( y \)-values for the given \( x \)-values: -1, 0, and 3.

### 1. For \( x = -1 \):

\[
y = \sqrt{-2(-1) + 1} - 3
\]
\[
= \sqrt{2 + 1} - 3
\]
\[
= \sqrt{3} - 3 \approx 1.732 - 3 \approx -1.268
\]

### 2. For \( x = 0 \):

\[
y = \sqrt{-2(0) + 1} - 3
\]
\[
= \sqrt{0 + 1} - 3
\]
\[
= \sqrt{1} - 3
\]
\[
= 1 - 3 = -2
\]

### 3. For \( x = 3 \):

\[
y = \sqrt{-2(3) + 1} - 3
\]
\[
= \sqrt{-6 + 1} - 3
\]
\[
= \sqrt{-5} - 3
\]

Since the square root of a negative number is not defined in the set of real numbers, there is no real value for \( y \) when \( x = 3 \).

### Summary of the Table:

| \( x \) | \( y \) |
|------------|--------------------------|
| -1 | \( \sqrt{3} - 3 \approx -1.268 \) |
| 0 | -2 |
| 3 | Not defined (Complex) |

Thus, the completed table is:

| \( x \) | \( y \) |
|------------|--------------------------|
| -1 | \(-1.268\) |
| 0 | \(-2\) |
| 3 | Not defined |