There are many instances in which the equation of a polynomial function could end up giving an incorrect answer because it does not take into account certain important inputs. This kind of problem is commonly encountered in the area of finance and business. As a matter of fact, these types of errors are extremely common in many different areas and are made due to either lack of knowledge of the topic or laziness. Let us now see how one can deal with this issue so that you don’t make the same mistakes.

The first step to analyze the **end behavior of polynomial functions** is to identify the starting point for the graph, which is called the beginning term. The starting point is often known as the initial value, because it represents the exact value of all the terms involved in the function after the initial term. To identify the end behavior of polynomial functions, consider the initial value of all the terms. It is easy to see that as the value of x gets bigger or smaller, the behavior of the curve is also changing. For this reason, it is advisable to plot out the graph as a way to get a handle on the starting point, which will give you the best way to analyze the behavior of the curve.

The second step is to plot out the intercepts on the function. Intercepts here refer to the change in the slope of y intercept as it moves from one value to the other. When analyzing the end behavior of polynomial functions where there are multiple terms, it is good to plot out the intercepts on one axis and the data on another axis. This makes it easier to focus on the plotted region.

The third step is to set up the main relationship between the x coordinate and the y coordinate for the two functions. If you plot out the data like this: A = (x-intercept), B = (y-intercept), C = (zoom in on either x or y), then zeros denote the functions of magnitude one or zero, respectively. For instance, if A(x) is the intercept of y, then zeros stand for the corresponding intercepts of x at any point along the x direction. This gives us the definition of the Poisson distribution, which we’ll use to analyze the behavior of these polynomial functions as follows:

The fourth step to validating this hypothesis is to plot out the intercept and the standardized mean. When analyzing graphs with multiple correlated variables, it is necessary to set up a hypothesis and postulates so that you can validly compare the behaviors of the variables over time. For instance, in a data set where the x variable is correlated with the y variable by a significant amount, we can conclude that there is a significant relationship between the x variable and a variable by drawing lines from the zero mean to the larger value of the x value at any point in time, say, plot the function curve of log10(x) against the log10(y). Once you see a point on the curve where the slope is positive, you are therefore concluding that the y variable is important, and the data points are showing you the standardized mean.

Once you have verified that hypothesis, you can plot out the plotted curves in the figure without bound. You can set the x-axis to zero, but since the data sets have been recorded over time, you don’t really need to do anything else with them other than set the x-axis to its own value. By plotting the data without bound, you can clearly see the** end behavior of polynomial functions** without bind. The points on the graph will not change any time when the output variable is changing. This clearly shows that the function does not need any bound, and hence the conclusion that it doesn’t need any calibration at all.

## End Behavior of Polynomial Functions

The end behavior of polynomial functions is quite complex, but for our purposes let us consider a simple example using the Fibonacci calculator. For every digit (n) in the input you give, the following number will be n times the digit (i.e. 360) times the digit (i.e. 7.5).

To determine the end behavior of polynomial functions, look at the left most term of their logarithm function. That term is called the dominant factor. As the value of the dominant factor increases, the resulting value of the logarithm will also increase, until it reaches the end behavior of polynomial functions when the logarithm of all the terms is equal to one. This is because as x becomes large or small, the slope of the logarithm curve will also change, depending upon whether the dominant factor is small or large. In the Fibonacci calculator example, this means that the slope of the logarithm function as x increases or decreases is always equal to one.

An important part of studying the end behavior of polynomial functions is that of identifying a turning point. A turning point is when, after some period of time, the rate of growth of the function is exactly what has been anticipated by the creator of it, given some initial conditions. For instance, in the Fibonacci calculator example this would happen when the slope of the logarithm function as x increases or decreases to the point where the function is being graphed as a function of x versus time. By finding these turning points, it becomes possible to study the evolution of this type of function over time, and to understand its behavior.