Rational Function In Precalculus Algebra
Dealing with Rational Functions
Recently in Precalculus Algebra at Wake Tech, we have been working extensively with analyzing and graphing ration functions. Rational functions are expressed in the form of fractions in which both the numerator and the denominator are polynomials. In other words, these functions have x in both the top and bottom of the fraction. Before many rational functions can be properly analyzed and deciphered, they must first be completely simplified, which often times includes factoring polynomials that exist within the function. Furthermore, the dual purpose of this writing assignment is to both test us to ensure that we understand information related to rational functions, while simultaneously reaffirming this information into our minds through practice. This lab will help my classmates and me to better understand the concepts of analyzing, deciphering, and graphing rational functions.
For the purposes of this writing assignment, we will be working with the example ,((x^2+12x+35))/((x^2+8x+15)). As aforementioned, the first step when analyzing this rational function is to factor both the numerator and the denominator of the
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In order to find these values, you will need to focus only on the numerator of the function when it is in factored form. Similarly to finding the restrictions to the domain, each of the factors in the numerator are set equal to zero, unless that factor is also in the denominator of the equation. So for this example that would leave us with (x+7) since (x+5) is also in the denominator. After setting, x+7=0, we can determine that the x-intercept of the graph is at, (-7,0). In the context of this example this means that when this rational function is graphed, it will cross the x-axis at
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