The limiting behavior of a function describes what happens to the function as x → ±∞. The degree of a polynomial and the sign of its leading coefficient dictates its limiting behavior.

Polynomial Functions.

Degree of the polynomial | Leading coefficient | |
---|---|---|

+ | – | |

Even | f(x) → ∞ as x → ±∞ |
f(x) → -∞ as x → ±∞ |

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Contents

- 1 What is the coefficient F?
- 2 Can the leading coefficient of f be negative?
- 3 What is the leading coefficient?
- 4 What is the sign of the leading term?
- 5 What is the symbol for the coefficient of friction?
- 6 What factors affect the coefficient of friction?
- 7 How do you know if a leading coefficient is positive?
- 8 How do you know if the leading coefficient is positive or negative?
- 9 How do you tell if a leading coefficient is positive or negative from a graph?
- 10 What is a leading coefficient and degree?
- 11 How do you find the leading term and leading coefficient of a degree?

## What is the coefficient F?

F (coefficient of inbreeding): F is the symbol for the coefficient of inbreeding, a way of gauging how close two people are genetically to one another. The coefficient of inbreeding, F, is the probability that a person with two identical genes received both genes from one ancestor.

## Can the leading coefficient of f be negative?

Example: Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function f(x)=−x3+5x. Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right as shown in the figure.

## What is the leading coefficient?

In a polynomial function, the leading term is the term containing the highest power of x. The coefficient of the leading term is called the leading coefficient.

## What is the sign of the leading term?

In a polynomial, the leading term is the term with the highest power of x. For example, the leading term of 7+x−3×2 is −3×2. The leading coefficient of a polynomial is the coefficient of the leading term. In the above example, the leading coefficient is −3.

## What is the symbol for the coefficient of friction?

This constant ratio is called the coefficient of friction and is usually symbolized by the Greek letter mu (μ). Mathematically, μ = F/L.

## What factors affect the coefficient of friction?

The friction force depends on two factors:

- a) The materials that are in contact. The two materials and the nature of their surfaces.
- b) The force pushing the two surfaces together. Pushing the surfaces together causes the more of the asperities to come together and increases the surface area in contact with each other.

## How do you know if a leading coefficient is positive?

If the leading coefficient is positive the function will extend to + ∞; whereas if the leading coefficient is negative, it will extend to – ∞.

## How do you know if the leading coefficient is positive or negative?

If the leading coefficient is positive, bigger inputs only make the leading term more and more positive. The graph will rise to the right. If the leading coefficient is negative, bigger inputs only make the leading term more and more negative.

## How do you tell if a leading coefficient is positive or negative from a graph?

The degree and leading coefficient of a polynomial always explain the end behavior of its graph:

- If the degree of the polynomial is even and the leading coefficient is positive, both ends of the graph point up.
- If the degree is even and the leading coefficient is negative, both ends of the graph point down.

## What is a leading coefficient and degree?

The highest power of the variable that occurs in the polynomial is called the degree of a polynomial. The leading term is the term with the highest power, and its coefficient is called the leading coefficient.

## How do you find the leading term and leading coefficient of a degree?

Explanation:

- The degree is the sum of the exponents on all terms.
- The leading term of a polynomial is just the term with the highest degree, and we see this is 3×5.
- The leading coefficient is just the number multiplying the highest degree term.
- The constant term is just a term without a variable.