Question

the polynomial function $f(x)$ is graphed below. fill in the form below regarding the features of this graph.
answer attempt 1 out of 2
the degree of $f(x)$ is odd and the leading coefficient is. there are different real zeros and relative maximums.

Explanation:

Step1: Analyze leading coefficient sign

As $x\to+\infty$, $f(x)\to+\infty$; as $x\to-\infty$, $f(x)\to-\infty$. For odd-degree polynomials, this means the leading coefficient is positive.

Step2: Count distinct real zeros

Count x-axis intersections: the graph crosses the x-axis at 5 distinct points, so there are 5 different real zeros.

Step3: Count relative maximums

Identify "peaks" on the graph: there are 3 upward-curving to downward-curving turning points, so 3 relative maximums.

Answer:

The degree of $f(x)$ is odd and the leading coefficient is positive. There are 5 different real zeros and 3 relative maximums.