Use the image to answer the question.

A curved line is graphed on a coordinate plane. The x-axis ranges from negative 5 to 5 in increments of 1. The y-axis ranges from negative 200 to 200 in increments of 100.

Use an input-output table to determine whether the graph accurately displays the function f(x)=4x3−x
using the inputs of −3
, −2
, −1
, 0, and 1.

Enter 1 if the graph is accurate.

Enter 2 if the graph is not accurate.

(1 point)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

To determine if the graph accurately displays the function \( f(x) = 4x^3 - x \), we can calculate the values of \( f(x) \) for the given inputs of \( -3, -2, -1, 0, \) and \( 1 \) and use an input-output table.

Calculating \( f(x) \):

1. For \( x = -3 \):
\[
f(-3) = 4(-3)^3 - (-3) = 4(-27) + 3 = -108 + 3 = -105
\]

2. For \( x = -2 \):
\[
f(-2) = 4(-2)^3 - (-2) = 4(-8) + 2 = -32 + 2 = -30
\]

3. For \( x = -1 \):
\[
f(-1) = 4(-1)^3 - (-1) = 4(-1) + 1 = -4 + 1 = -3
\]

4. For \( x = 0 \):
\[
f(0) = 4(0)^3 - 0 = 0
\]

5. For \( x = 1 \):
\[
f(1) = 4(1)^3 - 1 = 4(1) - 1 = 4 - 1 = 3
\]

Now we have the following input-output table:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-3 & -105 \\
-2 & -30 \\
-1 & -3 \\
0 & 0 \\
1 & 3 \\
\hline
\end{array}
\]

Now, if you can compare these values with the corresponding points on the graph, we can determine if the graph is accurate or not. Based on this table:

- Verify the points \((-3, -105)\), \((-2, -30)\), \((-1, -3)\), \( (0, 0) \), and \((1, 3)\) on the graph.

If all calculated points correspond to the points on the graph, then you would enter **1**. If any of these points do not match the graph, then you would enter **2**.

Since I cannot see the graph itself, I will instruct you to compare the values based on the calculations provided, and you can make the decision based on the comparison.