In order to better understand the bird problem, we need to understand a specific type of function. With the even-power function, as the input increases or decreases without bound, the output values become very large, positive numbers.
The coefficient is 1 (positive) and the exponent of the power function is 8 (an even number). An oil pipeline bursts in the Gulf of Mexico, causing an oil slick in a roughly circular shape. Because of the form of a polynomial function, we can see an infinite variety in the number of terms and the power of the variable. Identify the degree, leading term, and leading coefficient of the following polynomial functions. Identify the degree, leading term, and leading coefficient of the polynomial ?f(x)=4 x 2 ? x 6 +2x?6.
Knowing the degree of a polynomial function is useful in helping us predict its end behavior. Describe the end behavior and determine a possible degree of the polynomial function in [link].
We can tell this graph has the shape of an odd degree power function that has not been reflected, so the degree of the polynomial creating this graph must be odd and the leading coefficient must be positive. Describe the end behavior, and determine a possible degree of the polynomial function in [link].
In addition to the end behavior of polynomial functions, we are also interested in what happens in the “middle” of the function. A turning point of a graph is a point at which the graph changes direction from increasing to decreasing or decreasing to increasing. A continuous function has no breaks in its graph: the graph can be drawn without lifting the pen from the paper. What can we conclude about the polynomial represented by the graph shown in [link] based on its intercepts and turning points? Access these online resources for additional instruction and practice with power and polynomial functions. The behavior of a graph as the input decreases beyond bound and increases beyond bound is called the end behavior.
A polynomial function is the sum of terms, each of which consists of a transformed power function with positive whole number power.


The degree of a polynomial function is the highest power of the variable that occurs in a polynomial. The end behavior of a polynomial function is the same as the end behavior of the power function represented by the leading term of the function. The coefficient of the power function is the real number that is multiplied by the variable raised to a power. If a polynomial function is in factored form, what would be a good first step in order to determine the degree of the function? In general, explain the end behavior of a power function with odd degree if the leading coefficient is positive.
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End Behavior refers to the behavior of a graph as it approaches either negative infinity, or positive infinity.
One of the things math geeks get all jazzed about in Calculus is seeing what happens when and . We can do this with these rational function critters, too.  The key here is that horizontal (or slant) asymptote.
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A power function is a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number.
Notice that these graphs have similar shapes, very much like that of the quadratic function in the toolkit. The slick is currently 24 miles in radius, but that radius is increasing by 8 miles each week. A polynomial function consists of either zero or the sum of a finite number of non-zero terms, each of which is a product of a number, called the coefficient of the term, and a variable raised to a non-negative integer power. Although the order of the terms in the polynomial function is not important for performing operations, we typically arrange the terms in descending order of power, or in general form. For any polynomial, the end behavior of the polynomial will match the end behavior of the term of highest degree. As with all functions, the y-intercept is the point at which the graph intersects the vertical axis. This means the graph has at most one fewer turning point than the degree of the polynomial or one fewer than the number of factors.
We can also use this model to predict when the bird population will disappear from the island. However, as the power increases, the graphs flatten somewhat near the origin and become steeper away from the origin. Again, as the power increases, the graphs flatten near the origin and become steeper away from the origin.
We want to write a formula for the area covered by the oil slick by combining two functions.
The degree of the polynomial is the highest power of the variable that occurs in the polynomial; it is the power of the first variable if the function is in general form. A turning point is a point at which the function values change from increasing to decreasing or decreasing to increasing.
In this section, we will examine functions that we can use to estimate and predict these types of changes. The leading term is the term containing the highest power of the variable, or the term with the highest degree.



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