Question

To graph the square root function y=−2x+1−−−−√−3 , complete the table of data points for the funciton. when x is -1, 0, and 3.

Answer 1

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

Let's compute each case step by step.

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

\[
y = \sqrt{-2(-1) + 1} - 3
\]
\[
= \sqrt{2 + 1} - 3
\]
\[
= \sqrt{3} - 3
\]
This is approximately \( 1.732 - 3 = -1.268 \) (exact value: \( \sqrt{3} - 3 \)).

2. **When \( x = 0 \):**

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

3. **When \( x = 3 \):**

\[
y = \sqrt{-2(3) + 1} - 3
\]
\[
= \sqrt{-6 + 1} - 3
\]
\[
= \sqrt{-5} - 3
\]
Since the square root of a negative number is not defined in the set of real numbers, this means \( y \) is not defined at \( x = 3 \).

Now, we can summarize the calculated points in a table format:

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

So, the data points for the function when \( x = -1, 0, 3 \) are approximately:

- \( (-1, -1.268) \)
- \( (0, -2) \)
- \( (3, \text{undefined}) \)