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# This particular mathematics graph interpretation will discuss how graph of differs from and. The purpose of this project is to study the relationship among those functions.

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Introduction

Introduction

This particular mathematics graph interpretation will discuss how graph of differs from and . The purpose of this project is to study the relationship among those functions. The guiding question is: How do they differ from one another and what patterns do they have?

Hypothesis

The function will differ from the other function by having all the parts of the function below the x-axis, where negative units lie for y – axis, as a horizontal reflection. Because absolute value can only have positive value as a result, the function will also have positive value only. Therefore, when having an absolutely value graph, because only positive value exists, the negative value part of the graph will reflect upon x –axis. In addition, the original graph’s y – intercept and range will have positive sign of the original value and be equal to or greater than zero respectively for absolute value function.   Comparing and Absolute value graph of and         General Statement

When changing the equation from to , the bottom part (the part where y has a negative value)

Middle

and      The graph above is when the graph of and which is drawn in bold line are drawn together. By looking at the graph, it is clear that the function of ’s negative y-value part reflects upon x-axis to form the graph of absolute value. It makes x-intercepts, domain and asymptote for both of the function to remain the same while the y-intercept changes its sign because of the absolute value. However, if the graph had asymptotes, the function of absolute value and the original function will have the same asymptote except that the asymptote for function of absolute value will only work in 2nd and 3rd quadrants. Also, because it has done horizontal reflection, the range becomes . Therefore, the conjecture is always true and any function will obey this pattern.

Drawing graph on given graph of  Comparing and Hypothesis

Unlike the relationship between and graphs, the function will differ from the other function by having all the left part of the function about y-axis, where negative units lie for x – axis, as vertical reflection.

Conclusion : the part of the graph of 1st and 4th quadrant of reflects upon y-axis. It makes x-intercept, domain and asymptote to change and y – intercept to remain the same. Furthermore, because the function of absolute value has done vertical reflection, the range will start from the minimum or maximum point of the 1st and 4th quadrants of the graph. Therefore, the conjecture is always true and any function will obey this pattern.

Drawing graph on given graph of  Conclusion

After comparing these functions, it was noticeable that an absolute value makes significant differences in the graphs. When comparing and , it was found that the negative y-value part of the graph reflects upon the x-axis because an absolute value creates only positive values, and negative values can never exist. When comparing and , it was found that the positive x-value part of the graph reflects upon the y-axis, because the absolute value of “x” always creates the positive value of “y” regardless of x-value’s sign. Therefore, these functions differ from each other, and the function of the absolute value of either the whole function or the x-value only, each has its own specific patterns.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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