Question

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.

Answer 1

To determine whether the graph accurately displays the function \( f(x) = 4x^3 - x \), we need to calculate the output values for the given inputs: \( -3, -2, -1, 0, 1 \).

Let's calculate \( f(x) \) for each input:

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 summarize the input-output pairs:

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

Now, compare these values with the graph. If the corresponding points on the graph match these calculated values, then the graph is accurate. If any point does not match, then the graph is not accurate.

Based on your inspection of the graph, enter:

- **1** if the graph is accurate.
- **2** if the graph is not accurate.

Without seeing the graph, I can't determine the answer directly; you will need to match the calculated values with the graph to make your decision.