Question

PLZ HELP Describe the end behavior and determine whether the graph represents an odd-degree or an even-degree polynomial function. Then state the number of real zeros. simple answer

Answer 1

Answer:

End behavior: $f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty$  and $f(x)\rightarrow \infty\text{ as }x\rightarrow \infty$

The function has odd-degree.

The number of real zeros in 5.

Step-by-step explanation:

From the given graph it is clear that the graph approaches towards negative infinite as x approaches towards negative infinite.

$f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty$

The graph approaches towards positive infinite as x approaches towards positive infinite.

$f(x)\rightarrow \infty\text{ as }x\rightarrow \infty$

For even-degree the polynomial has same end behavior.

For odd-degree the polynomial has different end behavior.

Since the given functions has different end behavior, therefore the graph represents an odd-degree polynomial function.  

If the graph of a function intersects the x-axis at a point then it is a zero of the function.

If the graph of a function touch the x-axis at a point and return then it is a zero of the function with multiplicity 2. It means, the function has 2 equal zeros.

The graph intersect the x -axis at 3 points and it touch the x-axis at origin. So, the number of zeros is

$N=3+2=5$

The number of real zeros is 5.

Answer 2

Answer:

x=8

Step-by-step explanation:

6. an odd-degree polynomial function.

   f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

Step by step explanation;

6. The graph represent an odd-degree polynomial function.

The graph enters the graphing box from the bottom and goes up leaving through the top of the graphing box.This is a positive polynomial whose limiting behavior is given by;

f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞