Assignment #1
Nicole Mosteller
EMAT 6680

Investigation #1: Examine the following equation. What happens if the 4 is replaced by other numbers (not necessarily integers)? Interprete your findings.

Graphing Calculator 3.1 easily provides the graph of the equation.

There are several aspects of this graph that should be noted. The first property that I noticed was that it is symmetric about the origin. This made me begin to wonder how changing the numerical values of the equation would alter its symmetric property. We know that the intercepts along the x-axis are caused by setting the left side equal to zero, and the x-intercepts will change by altering the "4" in the original equation. Like wise, the intercepts along the y-axiz are caused by setting the right side equal to zero, and so altering the "1" will change the intercepts as well. To better explain what occurs with this relation, let's use the following as the general form for this equation:

.

Below are additional investigation pages that show the changes that occur

when a and b are altered.

Part 1: Let a and b be rational numbers greater than 0.

Part 2: Let a and b be equal to 1.

Part 3: Let a and b be equal to 0.

Part 4: Let a and b be rational numbers less than 0.

Part 5: View the evolution of the equation.

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