Question
Predict the end behavior of the graph of the function.
f(x)equals3.18x Superscript 4plus 6x squaredplusxnegative 6
f(x)equals3.18x Superscript 4plus 6x squaredplusxnegative 6
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To analyze the end behavior of the polynomial function
\[
f(x) = 3.18x^4 + 6x^2 + x - 6,
\]
we need to look at the leading term of the polynomial, as this term will dominate the function's behavior for very large and very small values of \(x\).
1. **Identify the leading term**: The leading term in this function is \(3.18x^4\), which is the term with the highest exponent (degree 4).
2. **Analyze the leading coefficient and degree**:
- The degree of the polynomial is 4 (an even degree).
- The leading coefficient (3.18) is positive.
3. **Determine end behavior**:
- For an even degree polynomial with a positive leading coefficient, the end behavior is as follows:
- As \(x \to +\infty\) (as \(x\) approaches positive infinity), \(f(x) \to +\infty\) (the graph will rise).
- As \(x \to -\infty\) (as \(x\) approaches negative infinity), \(f(x) \to +\infty\) (the graph will also rise).
In conclusion, the end behavior of the function \(f(x)\) is:
- \(f(x) \to +\infty\) as \(x \to +\infty\)
- \(f(x) \to +\infty\) as \(x \to -\infty\)
The graph will rise to the right and rise to the left.
\[
f(x) = 3.18x^4 + 6x^2 + x - 6,
\]
we need to look at the leading term of the polynomial, as this term will dominate the function's behavior for very large and very small values of \(x\).
1. **Identify the leading term**: The leading term in this function is \(3.18x^4\), which is the term with the highest exponent (degree 4).
2. **Analyze the leading coefficient and degree**:
- The degree of the polynomial is 4 (an even degree).
- The leading coefficient (3.18) is positive.
3. **Determine end behavior**:
- For an even degree polynomial with a positive leading coefficient, the end behavior is as follows:
- As \(x \to +\infty\) (as \(x\) approaches positive infinity), \(f(x) \to +\infty\) (the graph will rise).
- As \(x \to -\infty\) (as \(x\) approaches negative infinity), \(f(x) \to +\infty\) (the graph will also rise).
In conclusion, the end behavior of the function \(f(x)\) is:
- \(f(x) \to +\infty\) as \(x \to +\infty\)
- \(f(x) \to +\infty\) as \(x \to -\infty\)
The graph will rise to the right and rise to the left.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.