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Function Rules, Tables, and Graphs 2000 Views
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Description:
Looking to find function formulas from tables? We've got all you need, right here in this video.
Transcript
- 00:04
Function Rules, Tables, and Graphs, a la Shmoop.
- 00:11
Jack and Jill went up the hill to fetch a pail of water...
- 00:14
...because they’d entered a habanero-eating contest.
- 00:17
Too bad the troll will only let them drink if they find and graph the function of the hill’s incline.
- 00:24
The troll provides a table of points on the hill.
Full Transcript
- 00:28
(0,3), (-1,1), and (1,5)
- 00:32
Jack and Jill seem a little preoccupied, so let’s give them a hand before they really
- 00:36
burn their mouths.
- 00:38
First, let's draw our coordinate axes, x and y.
- 00:41
We can plot the points on a graph..and when we connect the dots, we can see that a line emerges.
- 00:48
To find the function rule of the line, we can use the slope intercept form of a line:
- 00:54
y equals mx plus b.
- 00:57
To calculate m, the slope, we need to find the rise and run between two points on the line.
- 01:03
So let’s use (0,3) and (1,5).
- 01:13
Slope equals rise…
- 01:15
...the distance between the y-points…
- 01:17
...over run...
- 01:19
…the distance between the two x-points.
- 01:22
When we plug in our two points, we get 5 minus three, over 1 minus 0.
- 01:29
Or 2 over 1.
- 01:30
Also known as 2.
- 01:39
Now our equation is y equals 2x plus b.
- 01:42
b represents the y-intercept, or the y-value when x equals 0.
- 01:47
The troll gave us this point.
- 01:49
The y-intercept is 3.
- 01:51
Which makes our equation y equals 2x plus 3.
- 01:55
Open sesame!
- 01:57
Now Jack and Jill can go find water at the bottom of the well.
- 02:00
Thanks, Troll.
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