To graph the cube root function y=12x−1−−−−√3+4

Question

, 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 \( x = 2 \), \( y \approx 6.843 \)