Tables
| Site: | Farwell |
| Course: | Michigan Algebra I Sept. 2012 |
| Book: | Tables |
| Printed by: | Guest user |
| Date: | Sunday, November 24, 2024, 3:21 AM |
Description
Writing a Function Rule
You can write a rule for a function by analyzing a table of values. Two ways to do this include finding the values to use slope-intercept form and finding the first difference.
To write a function rule in slope-intercept form, first choose two points on a line and use the slope formula to find the slope. Next, substitute one point into the equation and solve for b.
Example
Write the function rule for the line that models {(1, 3), (2, 4), (3, 5), (4, 6)}
Step 1. Choose any two points to find slope.
Not available in this example
Step 3. Since the y-intercept was not given, select any point and substitute in the x and y values in to y = mx + b to solve for b.
Using the point (1, 3)
Step 4. Substitute the values for m and b into y = mx + b to create the function rule.
Video Lesson
To learn how to write a function rule, select the following link:
First Difference
When looking at a table of values, the "finite differences" can be used to find the degree of a polynomial and then write a function rule. When looking at linear equations, the finite difference is called the "first difference." The first difference is the difference in y values of a given function. If the difference between each y value is constant, the function will be linear.
The formula y = ax + b is used to write a function rule using first difference. Where "a" corresponds to the value of the first difference and b is the y-intercept, (0, b).
Example
Write the equation for the function that contains the points in the table below.
Step 1. Make sure the x-values have a constant change.
3 - 2 = 1
2 - 1 = 1, etc.
Yes: 1
Step 2. Find the change from one y-value to the next.
-8-(-2) = -6
-2 - 4 = -6, etc.
Step 3. Use the "first difference" to write a formula.
a = -6
y -intercept, b = (0, 10) as found in the table
y = -6x + 10
Video Lesson
To learn more about finite differences, select the following link:
Practice
Writing a Function from a Table Worksheet
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Answer Key
Writing a Function from a Table Answer Key
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Practice
Filling a Swimming Pool Worksheet
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Answer Key
Filling a Swimming Pool Answer Key
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Sources
Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project
Holt, Rinehart, & Winston. "Linear Functions." http://my.hrw.com/math06_07/
nsmedia/homework_help/alg2/alg2_ch06_09_homeworkhelp.html (accessed August 14, 2010