The equation my group had was y = 2^-x. We were instructed to make a table of values for ‘x’ equaling numbers -10 through 10. Then we had to plot the points on a graph to show the increase or decrease of values. For our equations, starting with x = 10 (having the smallest ‘y’ value) each of the values multiplied by 2 each time. This became more clear when ‘x’ equaled a negative number because the y values become whole numbers, instead of fractions, showing a greater increase between values/ points. Our graph looks almost like an ‘L’ shape. It looks like it does because of our equation, the negative exponent being a big influence in our ‘y’ value results. On the positive side of the ‘x’ axis the numbers are all fractions (really small numbers), which is why the graph points are all less than 1. On the negative side of the ‘x’ axis the numbers are whole numbers. This is because the exponent is negative. If the exponent is negative (-x) and the number your putting in as the ‘x’ value is negative your exponent will end up being positive (-(-10) = 10). The line increases dramatically on the negative side of the ‘x’ axis because the whole number are multiplying by 2 each time.
This exercise helped me understand integral exponents because it gave a clear visual representation of they work. I found it helpful to make the table of values and the graph because in the tables of values I could understand the difference between the values (i.e. 32 – 64 = multiplied by 2) and on the graph I could see a visual representation of that distance to help me understand how the jumps between values increase as the number get larger. It also helped me get a better understanding of negative exponents and how they work.
Our partner group had the equation y = 2^x. There graph was a reflection of ours. Their graph had really small numbers (fractions) on the negative side, and whole numbers on the positive side of the ‘y’ axis. This is because their equation had a positive exponent instead of a negative like ours. In conclusion their line on the graph was opposite to ours.
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