Ex: Graph a Linear Function Using a Table of Values — Transcript

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1. 0:00We want to complete the table using the function  rule F of x equals negative three x plus five and
2. 0:06then use the table to graph the function. We  did just finish studying linear equations,
3. 0:10so hopefully, we recognize this as a linear  function. But whether we do or not, we can always
4. 0:14graph a function by completing a t-table and then  applying the points to sketch the graph. If it's
5. 0:19helpful, we can replace F of x with Y. This is  equivalent to Y equals negative three x plus five.
6. 0:28Now we'll select values of x, perform  substitution, then determine the corresponding
7. 0:32function value or Y value. Let's select x  equals negative one, zero, one, two, and three.
8. 0:40So when x is equal to negative one, the function  value or corresponding y value would be negative
9. 0:48three times negative one plus five. This would be  positive three plus five, which is equal to eight,
10. 0:55which means the graph of our function will contain  the point with coordinates negative one and eight.
11. 1:01Now this point is off the screen, so we'll go  ahead and go to the next x value of zero. So
12. 1:06the y value would be negative three times  zero plus five, which is equal to five. So
13. 1:13the graph of our function will contain  the point zero five or this point here.
14. 1:20When x is equal to one, we'd have negative  three times one plus five. This will be
15. 1:26negative three plus five, that's positive two,
16. 1:29so the graph would contain the point with  coordinates one and two or this point here.
17. 1:38Next, we have x equals two, so we have  negative three times two plus five, which
18. 1:43is equal to negative six plus five, that's  negative one. So our function must contain
19. 1:49the point with an x coordinate of two and  a y coordinate of one, this point here.
20. 1:56And lastly, we have x equals three,  so the y coordinate would be negative
21. 2:01three times three plus five, which is  negative nine plus five, which is equal
22. 2:06to negative four. So the graph of our  function would contain the point with
23. 2:09an x coordinate of three and a y coordinate of  negative four, which would be this point here.
24. 2:15Now we can truly see that the  graph of our function will be a
25. 2:17line passing through these four points,  so it would look something like this.
26. 2:24Now, I should mention that if we recognize this  as a linear function in slope-intercept form
27. 2:28or Y equals M x plus B form, we should have  been able to graph this line without having
28. 2:35to complete a t-table. Remember that  B is the y-intercept, so in this case,
29. 2:39the y-intercept was five, and the slope of this  line is negative three or negative three over one.
30. 2:48So a faster way to graph the same line would  have been to plot the y-intercept here and then
31. 2:55knowing the slope was negative three over one,  we would have moved down three units and right
32. 3:00one unit to determine this point here. And of  course, we could have done that several times:
33. 3:04down three, right one, down three, right  one, and we could have found these points
34. 3:09much faster by using the information given  from the form of the linear function. We'll
35. 3:14now take a look at graphing several other  types of functions by completing a t-table.