Question
Use the input-output table to determine the graph is accurately displayed the function f(x)= 4x^3-x using the inpoof -3, -2, -1 and 1
Answers
GPT-4o mini
To determine if the graph of the function \( f(x) = 4x^3 - x \) is accurately displayed, we can evaluate the function at the given input values: -3, -2, -1, and 1. We'll calculate the output 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 \( x = 1 \)**:
\[
f(1) = 4(1)^3 - 1 = 4(1) - 1 = 4 - 1 = 3
\]
Now we have the input-output pairs:
- \( (-3, -105) \)
- \( (-2, -30) \)
- \( (-1, -3) \)
- \( (1, 3) \)
Using these pairs, you can plot the points on a graph and check them against the displayed graph of the function \( f(x) = 4x^3 - x \). Make sure the points align with what is displayed on the graph. If they do, then the graph is accurately representing the function at these points. If there are discrepancies, then the graph may not correctly represent the function.
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 \( x = 1 \)**:
\[
f(1) = 4(1)^3 - 1 = 4(1) - 1 = 4 - 1 = 3
\]
Now we have the input-output pairs:
- \( (-3, -105) \)
- \( (-2, -30) \)
- \( (-1, -3) \)
- \( (1, 3) \)
Using these pairs, you can plot the points on a graph and check them against the displayed graph of the function \( f(x) = 4x^3 - x \). Make sure the points align with what is displayed on the graph. If they do, then the graph is accurately representing the function at these points. If there are discrepancies, then the graph may not correctly represent the function.