Question

To graph the cube root function y=13x−3−−−−√3+2
, complete the table of data points for the function.(2 points)
x y
2
3
4

Answer 1

To complete the table of data points for the function \( y = \sqrt[3]{13x - 3} + 2 \), we can calculate the values of \( y \) for each given \( x \) value:

### Given Function
\[ y = \sqrt[3]{13x - 3} + 2 \]

### x = 2
\[
y = \sqrt[3]{13(2) - 3} + 2 \\
y = \sqrt[3]{26 - 3} + 2 \\
y = \sqrt[3]{23} + 2 \\
y \approx 2.843 + 2 \approx 4.843
\]

### x = 3
\[
y = \sqrt[3]{13(3) - 3} + 2 \\
y = \sqrt[3]{39 - 3} + 2 \\
y = \sqrt[3]{36} + 2 \\
y \approx 3.301 + 2 \approx 5.301
\]

### x = 4
\[
y = \sqrt[3]{13(4) - 3} + 2 \\
y = \sqrt[3]{52 - 3} + 2 \\
y = \sqrt[3]{49} + 2 \\
y \approx 3.659 + 2 \approx 5.659
\]

### Completed Table
Now, the completed data points for the table are:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
2 & \approx 4.843 \\
3 & \approx 5.301 \\
4 & \approx 5.659 \\
\hline
\end{array}
\]

You can round the \( y \) values to a suitable decimal place as needed. If you need further assistance, let me know!