Question

To graph the cube root function y=2x−1−−−−√3+2
, complete the table of data points for the function .(2 points)
x y
0
1
2

Answer 1

To complete the table for the cube root function \( y = 2\sqrt[3]{x} + 2 \), we will calculate \( y \) for each given \( x \) value.

1. For \( x = 0 \):
\[
y = 2\sqrt[3]{0} + 2 = 2(0) + 2 = 2
\]

2. For \( x = 1 \):
\[
y = 2\sqrt[3]{1} + 2 = 2(1) + 2 = 2 + 2 = 4
\]

3. For \( x = 2 \):
\[
y = 2\sqrt[3]{2} + 2 \approx 2(0.7937) + 2 \approx 1.5874 + 2 \approx 3.5874
\]

Now we can fill in the table:

| x | y |
|-----|-----------|
| 0 | 2 |
| 1 | 4 |
| 2 | approximately 3.59 |

Thus, the final values for the table will be:

- At \( x = 0 \), \( y = 2 \)
- At \( x = 1 \), \( y = 4 \)
- At \( x = 2 \), \( y \approx 3.59 \) (more accurately, \( y \approx 3.5874 \))