Questions: The degree of f(x) is □ and the leading coefficient is □ . There are □ distinct real zeros and □ relative maximums.

Transcript text: Answer Attempt 1 out of 2 The degree of $f(x)$ is $\square$ and the leading coefficient is $\square$ . There are $\square$ distinct real zeros and $\square$ relative maximums.

Solution

Solution Steps

Step 1: Determine the Degree of f(x)

The degree of a polynomial function is the highest power of the variable $ x $. By observing the graph, we see that the function has three turning points, which suggests that the polynomial is of degree 4 (since a polynomial of degree $ n $ can have up to $ n-1 $ turning points).

Step 2: Determine the Leading Coefficient

The leading coefficient is the coefficient of the term with the highest degree. By observing the end behavior of the graph, we see that as $ x $ approaches positive and negative infinity, $ f(x) $ approaches negative infinity. This indicates that the leading coefficient is negative.

Step 3: Count the Distinct Real Zeros

Distinct real zeros are the points where the graph intersects the x-axis. By observing the graph, we see that it intersects the x-axis at 3 distinct points.

Step 4: Count the Relative Maximums

Relative maximums are the peaks of the graph. By observing the graph, we see that there are 2 relative maximums.