Questions: Describe the end behavior of the graph of the polynomial function.
f(x)=3x^5+4x^3-2x+5
Transcript text: Describe the end behavior of the graph of the polynomial function.
\[
f(x)=3 x^{5}+4 x^{3}-2 x+5
\]
Solution
Solution Steps
Step 1: Determine the degree of the polynomial.
The degree of the polynomial is the highest power of x. In $f(x) = 3x^5 + 4x^3 - 2x + 5$, the highest power is 5.
Step 2: Determine the leading coefficient.
The leading coefficient is the coefficient of the term with the highest power of x. In the given polynomial, the leading coefficient is 3.
Step 3: Analyze the degree and leading coefficient to describe the end behavior.
Since the degree is odd (5) and the leading coefficient is positive (3), the end behavior is as follows: as x approaches negative infinity, f(x) approaches negative infinity; as x approaches positive infinity, f(x) approaches positive infinity. This corresponds to the graph falling to the left and rising to the right.