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Horizontal stretching of functions is a common technique used in algebra 2 homework problems. Proofs are typically drawn using this technique to reduce the amount of work, or at least make it less overwhelming. This blog post will walk the reader through the process of determining what horizontal stretching can be accomplished. It will also show some examples of how these methods are applied to write proofs for review questions on Algebra 2 homework assignments. As many students may experience with math, Algebra 2 was introduced with back-breaking workloads that require students to do more than one type of problem within every unit. Expository writing is often the most difficult of the lot, because it is not just about explaining what you are doing, but explaining why you are doing it. One useful tool in aiding in fully explaining why one chose to do a certain type of problem is horizontal stretching. This blog post will outline horizontal stretching for functions. The goal of this method is to reduce the number of steps needed to solve a given problem by increasing the amount of information available to analyze the subject matter. One great limitation of this method is that one must be very careful when using it on homework problems. There are many algorithms that can be employed to simplify proofs either unnoticed or improperly, hereby leading to incorrect or incomplete understanding of what was accomplished with this method. Let us begin by defining the variables used in this method. In essence, horizontal stretching is a way to transform a function from one form to another, in order to make the process of solving a problem easier. There are a number of different types of functions that can be horizontally stretched. One may take a rational function, and stretch it into an equivalent linear or absolute value form. It may also be stretched into an equivalent exponential form, either in the simplest case or with variable exponentiation added. Additionally, complex numbers can be used to transform both real-valued and rational functions into other forms. The stretch can be performed on a real-valued function ƒ(x). If the function is a rational function, it can be stretched into a linear form. Furthermore, if the rational function is a perfect square, the process of stretching the function may actually simplify it. If "ƒ"(x) = 1/2x + 1/4x + 1/8x+...= 0 (which is an example of an "equation"), then by simply multiplying both sides by 4, one may get rid of all fractions leaving only integers. This process allows one to avoid having to do long division to solve for y. Now suppose that instead of 1/4x+1/8x+... = 0, one had ƒ(x) = 2x − 3. This problem can equivalently be solved by multiplying both sides of the equation by 8. This process of multiplying both sides of the equation by an integer is known as horizontal stretching, and it is illustrated in this example graphically in the form of a graph. Now suppose that instead of 1/4x+1/8x+...= 0, one had ƒ(x) = −1 + 2·3/2·3/5·...= 0. This problem can equivalently be solved by squaring both sides to produce ƒ(2). eccc085e13
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