Question

To graph the cube root function y=5x+2−−−−√3−4 , complete the table of data points for the function.(2 points) x y −1 −2 −3

Answer 1

To graph the cube root function given by the equation \( y = 5\sqrt[3]{x} - 4 \), we will complete the table by calculating the value of \( y \) for each value of \( x \).

### Given equation:
\[
y = 5\sqrt[3]{x} - 4
\]

### Calculating values:

1. **For \( x = -1 \)**:
\[
y = 5\sqrt[3]{-1} - 4 = 5(-1) - 4 = -5 - 4 = -9
\]

2. **For \( x = -2 \)**:
\[
y = 5\sqrt[3]{-2} - 4 \approx 5(-1.2599) - 4 \approx -6.2995 - 4 \approx -10.2995 \approx -10.3 \text{ (rounded to one decimal)}
\]

3. **For \( x = -3 \)**:
\[
y = 5\sqrt[3]{-3} - 4 \approx 5(-1.442) - 4 \approx -7.21 - 4 \approx -11.21 \approx -11.2 \text{ (rounded to one decimal)}
\]

### Data Table:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-1 & -9 \\
-2 & -10.3 \\
-3 & -11.2 \\
\hline
\end{array}
\]

### Final Table for Data Points:
- For \( x = -1 \), \( y = -9 \)
- For \( x = -2 \), \( y = -10.3 \)
- For \( x = -3 \), \( y = -11.2 \)

Feel free to ask if you need further calculations or information!