Question

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

Explanation:

Step1: Determine degree parity

The graph rises as $x\to+\infty$ and rises as $x\to-\infty$, so the degree is even. The number of turning points is 3, so degree = turning points + 1 = $3+1=4$.

Step2: Identify leading coefficient sign

Since $f(x)\to+\infty$ as $x\to\pm\infty$, the leading coefficient is positive.

Step3: Count distinct real zeros

The graph crosses the $x$-axis 1 time, so there is 1 distinct real zero.

Step4: Count relative minima

The graph has 2 "valley" turning points, so there are 2 relative minima.

Answer:

The degree of $f(x)$ is $\boldsymbol{4}$ and the leading coefficient is $\boldsymbol{positive}$. There are $\boldsymbol{1}$ different real zeros and $\boldsymbol{2}$ relative minima.