This assignment allows us to explore some aspects of spreadsheet programs. I chose to construct a graph of any function y = f(x) by generating a table of values with the x values in one column and the y values in another. The spreadsheet program that I used was Excel. I chose a random f(x). The function I chose first was f(x) = (x/2)^2. I chose to look at this function for x values ranging from -10 to 10. The x and y values are below.

X | Y1 |

-10 | 25 |

-9 | 20.25 |

-8 | 16 |

-7 | 12.25 |

-6 | 9 |

-5 | 6.25 |

-4 | 4 |

-3 | 2.25 |

-2 | 1 |

-1 | 0.25 |

0 | 0 |

1 | 0.25 |

2 | 1 |

3 | 2.25 |

4 | 4 |

5 | 6.25 |

6 | 9 |

7 | 12.25 |

8 | 16 |

9 | 20.25 |

10 | 25 |

Intuition told me that this should be a parabola and the x and y values seem to support this. The graph should tell us more.

The graph seems to further support the claim that this is a parabola, and indeed it is.

The second function that I looked at was -(x/2)^2+x-1. The x and y values are below.

X | Y2 |

-10 | -36 |

-9 | -30.25 |

-8 | -25 |

-7 | -20.25 |

-6 | -16 |

-5 | -12.25 |

-4 | -9 |

-3 | -6.25 |

-2 | -4 |

-1 | -2.25 |

0 | -1 |

1 | -0.25 |

2 | 0 |

3 | -0.25 |

4 | -1 |

5 | -2.25 |

6 | -4 |

7 | -6.25 |

8 | -9 |

9 | -12.25 |

10 | -16 |

This, too, should be a parabola. The graph is below.

Indeed, this is also a parabola.

The last thing that I did was put these x and y values together and graphed the functions together. Below are the x and y values.

X | Y1 | Y2 |

-10 | 25 | -36 |

-9 | 20.25 | -30.25 |

-8 | 16 | -25 |

-7 | 12.25 | -20.25 |

-6 | 9 | -16 |

-5 | 6.25 | -12.25 |

-4 | 4 | -9 |

-3 | 2.25 | -6.25 |

-2 | 1 | -4 |

-1 | 0.25 | -2.25 |

0 | 0 | -1 |

1 | 0.25 | -0.25 |

2 | 1 | 0 |

3 | 2.25 | -0.25 |

4 | 4 | -1 |

5 | 6.25 | -2.25 |

6 | 9 | -4 |

7 | 12.25 | -6.25 |

8 | 16 | -9 |

9 | 20.25 | -12.25 |

10 | 25 | -16 |

And the two functions graphed together are below.