Question

To graph the cube root function y=12x−1−−−−√3+4
, complete the table of data points for the function. (2 points)
x y
0
1
2

Answer 1

To graph the function \( y = \sqrt[3]{12x - 1} + 4 \), we will calculate the corresponding \( y \) values for the given \( x \) values (0, 1, 2).

1. **For \( x = 0 \)**:
\[
y = \sqrt[3]{12(0) - 1} + 4 = \sqrt[3]{-1} + 4 = -1 + 4 = 3
\]

2. **For \( x = 1 \)**:
\[
y = \sqrt[3]{12(1) - 1} + 4 = \sqrt[3]{12 - 1} + 4 = \sqrt[3]{11} + 4
\]
The approximate value of \( \sqrt[3]{11} \) is about 2.223, so:
\[
y \approx 2.223 + 4 \approx 6.223
\]

3. **For \( x = 2 \)**:
\[
y = \sqrt[3]{12(2) - 1} + 4 = \sqrt[3]{24 - 1} + 4 = \sqrt[3]{23} + 4
\]
The approximate value of \( \sqrt[3]{23} \) is about 2.843, so:
\[
y \approx 2.843 + 4 \approx 6.843
\]

Now we can fill in the table:

| \( x \) | \( y \) |
|----------|----------|
| 0 | 3 |
| 1 | 6.223 |
| 2 | 6.843 |

Thus, the completed points are:
- At \( x = 0 \), \( y = 3 \)
- At \( x = 1 \), \( y \approx 6.223 \)
- At \( x = 2 \), \( y \approx 6.843 \)