Contents

- 1 How do you determine end behavior?
- 2 How do you determine far left and far right behavior?
- 3 What is the leading term of the polynomial function?
- 4 What are the characteristics of non polynomial functions?
- 5 What are some examples of behavior?
- 6 How to find the end behavior of a function?
- 7 What is the end behavior of a monomial function?

## How do you determine end behavior?

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

### How do you determine far left and far right behavior?

1. Determine the far-left and far-right behavior by examining the leading coefficient and degree of the polynomial. The sign of the leading coefficient determines if the graph’s far-right behavior. If the leading coefficient is positive, then the graph will be going up to the far right.

**What is the end behavior on the left side?**

In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

**How do you tell if end behavior is up or down?**

End Behavior: The degree is odd and the leading coefficient is positive, so the end behavior pattern is LEFT DOWN and RIGHT UP….

End Behavior | n is Even (not zero) | n is Odd |
---|---|---|

a is negative | Both Ends Down | Left Up, Right Down |

## What is the leading term of the polynomial function?

Leading Term. When the polynomial function is written in standard form, , the leading term is . In other words, the leading term is the term that the variable has its highest exponent.

### What are the characteristics of non polynomial functions?

Characteristics

- is not a polynomial because it has a variable under the square root.
- is not a polynomial because it has a variable in the denominator of a fraction.
- is not a polynomial because it has a fractional exponent.

**What is the leading term test?**

A leading term in a polynomial function f is the term that contains the biggest exponent. A coefficient is the number in front of the variable. The leading coefficient test is a quick and easy way to discover the end behavior of the graph of a polynomial function by looking at the term with the biggest exponent.

**What is left and right behavior?**

The left hand behavior of a polynomial function. If the degree of the polynomial is Odd, the left hand Changes from the right hand. If the degree of the polynomial is Even, the left hand does the Same as the right hand.

## What are some examples of behavior?

List of Words that Describe Behavior

- Active: always busy with something.
- Ambitious: strongly wants to succeed.
- Cautious: being very careful.
- Conscientious: taking time to do things right.
- Creative: someone who can make up things easily or think of new things.
- Curious: always wanting to know things.

### How to find the end behavior of a function?

Example: Find the end behavior of the function x 4 − 4 x 3 + 3 x + 25. The degree of the function is even and the leading coefficient is positive. So, the end behavior is: f ( x) → + ∞, as x → − ∞ f ( x) → + ∞, as x → + ∞. The graph looks as follows:

**How to determine the end behavior of a polynomial?**

The end behavior of a polynomial depends on the leading coefficient (the coefficient of the term with the greatest power) and the degree (the exponent of the term with the greatest power) of the polynomial. If the degree is even and the leading coefficient is positive, the graph of the polynomial rises left and rises right.

**When does the leading term change the end behavior?**

When the leading term is an odd power function, as x decreases without bound, f (x) also decreases without bound; as x increases without bound, f (x) also increases without bound. If the leading term is negative, it will change the direction of the end behavior. The table below summarizes all four cases.

## What is the end behavior of a monomial function?

Monomial functions are polynomials of the form , where is a real number and is a nonnegative integer. Let’s algebraically examine the end behavior of several monomials and see if we can draw some conclusions. 2) Consider the monomial .