In the first picture, the functions are linear, and all functions have zeroes of 0, because whenever x=0, y also equals zero.This means all lines intersect at (0,0), and it creates an interesting visual. The reflections in this image also create an interesting visual. If you reflect orange of the y-axis and the x-axis, you get purple. If you reflect orange across y=x, you get green. If you reflect Purple across y=x, you get blue. If you reflect blue across the y-axis and x-axis, you get green. If you reflect green across y=x, you get orange.
In the second picture, the picture is using asymptotes, at y=0 and x=0. All lines in one quadrant are either reflected over the x-axis, the y-axis, y=-x, or y=x, with lines in another quadrant. All equations are 1 divided by an a value multiplied by x. So, these equations only differ because of their steepness.
In the third picture, the graph uses exponential decay and exponential growth functions. There are also horizontal lines at y=1 and y=-1. This is because two of the functions being used are f(x)=1*1^x. Functions in this graph are also being reflected across the y-axis, x-axis, y=x, and y=-x.
The main ideas that inspired the the three graphs were patterns and reflection. The graphs I created for my final project differ greatly from my graph at the beginning of the trimester. At the beginning of the trimester, I did not really understand how graphs that were not linear worked, but now I have a great understanding, and it helped me design these graphs. Understanding how asymptotes and exponential graphs worked, really allowed me to create some interesting visuals.
In the second picture, the picture is using asymptotes, at y=0 and x=0. All lines in one quadrant are either reflected over the x-axis, the y-axis, y=-x, or y=x, with lines in another quadrant. All equations are 1 divided by an a value multiplied by x. So, these equations only differ because of their steepness.
In the third picture, the graph uses exponential decay and exponential growth functions. There are also horizontal lines at y=1 and y=-1. This is because two of the functions being used are f(x)=1*1^x. Functions in this graph are also being reflected across the y-axis, x-axis, y=x, and y=-x.
The main ideas that inspired the the three graphs were patterns and reflection. The graphs I created for my final project differ greatly from my graph at the beginning of the trimester. At the beginning of the trimester, I did not really understand how graphs that were not linear worked, but now I have a great understanding, and it helped me design these graphs. Understanding how asymptotes and exponential graphs worked, really allowed me to create some interesting visuals.