Questions: Use the leading-term test to match the function (f(x)=x^5+frac13 x-2) with one of the given graphs Choose the correct graph below. A. B. C. D.

$Use the leading-term test to match the function (f(x)=x^5+frac13 x-2) with one of the given graphs Choose the correct graph below. A. B. C. D.$

Transcript text: Use the leading-term test to match the function $f(x)=x^{5}+\frac{1}{3} x-2$ with one of the given graphs Choose the correct graph below. A. B. c. D.

Solution

Solution Steps

Step 1: Identify the leading term

The leading term of the polynomial $f(x) = x^5 + \frac{1}{3}x - 2$ is $x^5$.

Step 2: Determine the end behavior

Since the leading term is $x^5$, the degree is 5 (odd) and the leading coefficient is 1 (positive). Therefore, the end behavior of the graph is down to the left and up to the right.

Step 3: Match the graph

The only graph that exhibits this end behavior is B.