Answer:
End behavior: [tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty[/tex] and [tex]f(x)\rightarrow \infty\text{ as }x\rightarrow \infty[/tex]
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.
[tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty[/tex]
The graph approaches towards positive infinite as x approaches towards positive infinite.
[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow \infty[/tex]
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
[tex]N=3+2=5[/tex]
The number of real zeros is 5.
