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.

(1 point)
Remaining Attempts : 3

Answer 1

To determine whether the graph accurately displays the function \( f(x) = 4x^3 - x \), we should calculate the output values for the given input values: \( -3, -2, -1, 0, \) and \( 1 \). Then we can compare these values with the graph to see if they match.

Let's compute the function's values:

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 computed points:
- \( f(-3) = -105 \)
- \( f(-2) = -30 \)
- \( f(-1) = -3 \)
- \( f(0) = 0 \)
- \( f(1) = 3 \)

Next, compare these outputs with the values plotted on the graph at these x-values. If all calculated function values correspond to points on the graph:

- If they match, then the graph is accurate (enter **1**).
- If any do not match, the graph is not accurate (enter **2**).

Since I cannot see the graph itself, I recommend you compare the computed values against the graph. Based on your comparison, enter **1** if they match or **2** if they do not match.