Question

in exercises 23 and 24, use the graph to describe the degree and leading coefficient of ( f ).

Explanation:

Step1: Analyze end behavior of #23

The graph of $f$ has ends going in opposite directions: as $x\to+\infty$, $f(x)\to+\infty$; as $x\to-\infty$, $f(x)\to-\infty$. This means the degree is odd. The number of turning points is 2, so degree $>2$, minimum odd degree is 3. Since $x\to+\infty$, $f(x)\to+\infty$, the leading coefficient is positive.

Step2: Analyze end behavior of #24

The graph of $f$ has ends going in the same direction: as $x\to+\infty$, $f(x)\to+\infty$; as $x\to-\infty$, $f(x)\to+\infty$. This means the degree is even. The number of turning points is 3, so degree $>3$, minimum even degree is 4. Since both ends rise, the leading coefficient is positive.

Answer:

1. The degree of $f$ is an odd number (at least 3), and the leading coefficient is positive.
2. The degree of $f$ is an even number (at least 4), and the leading coefficient is positive.