Chapter 1
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| balance point | the point(x,y) with the x-coordinate that is the AVERAGE of all the x-coordinates in the table and with the y-coordinate that is the AVERAGE of all the y-coordinates in the table (p.44) Also known as a "centroid" in geometry.
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| closed-form definition | a function that lets you find any output [f(n)] for any input [n] by DIRECT calculation
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| cubic function | a function defined by a polynominal in which the highest-degree term is cubed, and generally looks like "ax^3+bx+c
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| difference table | a table that helps you see patterns that lead to recursive definitions p.10
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| hockey stick property | To find the next OUTPUT in a table, add (the sum of ALL the DIFFERENCES so far and the single FIRST OUTPUT of the table).
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| line of best fit | given a set of data, the line that minimizes the sum of the squares of the errors (or it minimizes the mean squared error), and contains the balance point.
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| mean absolute error | the average of the absolute values of the errors (or lengths of the outlier points from the line)
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| outlier | a data point (x,y) that lies outside, or far away, from the rest of the data
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| quadratic function | a function defined by a polynominal in which the highest-degree term is squared, and generally looks like "f(x)=ax^2+bx+c."
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| recursive definition | a function that expresses patterns in the outputs of a function p.9
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| Theorem 1.2 | If "f(x)=ax+b" is a linear function, its differences are constant.
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| Theorem 1.1 | An input-output table with a constant differences can be matched with a linear function. The slope of the graph is the constant difference in the table.
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| Rise/Run | change in output/change in input
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| Difference | the amount to add to move from one output to the next output
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| Up-and-over property | Add (the previous output and the difference) onto the next output when writing a recursive function
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| Theorem 1.3 | For any quadratic function, the second differences are constant. The constant second difference is 2a, (or twice the coefficient of the squared term).
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| factoral function, n! | a function that has a "n!" where "n!" is the product of all the intergers from 1 to n. This function has no simple closed form.
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Review the information in the table. When you are ready to quiz yourself you can hide individual columns or the entire table. Then you can click on the empty cells to reveal the answer. Try to recall what will be displayed before clicking the empty cell.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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Created by:
Fortier Family
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