Question

How do I describe the end behavior, determine if it's an odd or even degree, and the real number of zeros? Please help me.

Answer 1

Answer:

1. Even Degree

2. 6 zeros

Step-by-step explanation:

Determine if it’s an odd or even degree:—

  - The graph is shown approach positive infinity when both sides of x-values, negative and positive, both approach their respective infinity sides.

To put it simply, see when both negative x-values and positive x-values approach their negative or positive infinity, the y-values will always be positive, even if negative x-values approach negative infinity.

For a polynomial function to be an even degree, it must satisfy the following:—

$\displaystyle \large{ \lim_{x \to \pm \infty} f(x) = \infty}$

As an odd degree, either negative or positive x-values will approach positive infinity or negative infinity, depending on the function itself.

From the graph, we can say that the function is an even degree.

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Summary I

  Even-Odd Degree

Even Degree, when both sides of x-value approach their respective infinity, y-value will always approach positive infinity.

Odd Degree, one side of y-value will approach positive infinity and another will approach negative infinity.

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Determine numbers of zeros:—

  - We can determine numbers of zeros by examining x-axis and the graph. How many times does the graph intersect or pass through x-axis? Count and you should get 6 intercepts.

Therefore, there are 6 real solutions/zeros for this function/equation.

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Summary II

  Determine zeros

To determine or check how many solutions or zeros do the graph/function/equation has, you can use the graph method. Simply count how many times does the graph pass through x-axis and x-intercepts are zeros.

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If you have any doubts regarding my answer or explanation, do not hesitate to ask in comment!