Question

To graph the cube root function y=5^3√x+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 \( y = 5\sqrt[3]{x} + 2 - 3 - 4 \), we first simplify this expression. The function simplifies as follows:

\( y = 5\sqrt[3]{x} - 5 \)

Now, we will calculate the value of \( y \) for the specified \( x \) values (-1, -2, and -3):

1. For \( x = -1 \):
\[
y = 5\sqrt[3]{-1} - 5
\]
\(\sqrt[3]{-1} = -1\), so:
\[
y = 5(-1) - 5 = -5 - 5 = -10
\]

2. For \( x = -2 \):
\[
y = 5\sqrt[3]{-2} - 5
\]
To find \(\sqrt[3]{-2}\), we calculate:
\(\sqrt[3]{-2} \approx -1.26\), so:
\[
y = 5(-1.26) - 5 \approx -6.3 - 5 \approx -11.3
\]

3. For \( x = -3 \):
\[
y = 5\sqrt[3]{-3} - 5
\]
To find \(\sqrt[3]{-3}\), we calculate:
\(\sqrt[3]{-3} \approx -1.442\), so:
\[
y = 5(-1.442) - 5 \approx -7.21 - 5 = -12.21
\]

Now, we can complete the table of data points:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-1 & -10 \\
-2 & -11.3 \\
-3 & -12.21 \\
\hline
\end{array}
\]