1 00:00:00,217 --> 00:00:05,472 We're asked to graph the function f(x)=5x-4 2 00:00:05,472 --> 00:00:09,973 and we'll do it by really just sampling some points from the domain 3 00:00:09,973 --> 00:00:12,287 and seeing what value our function takes 4 00:00:12,287 --> 00:00:13,839 and then we'll just graph those points 5 00:00:13,839 --> 00:00:15,972 and then we'll just connect the dots and see what forms, 6 00:00:15,972 --> 00:00:17,189 and there's other ways to do this 7 00:00:17,189 --> 00:00:20,538 but this is kind of the most simple, or the most basic way. 8 00:00:20,538 --> 00:00:22,889 So if you look at this function over here, 9 00:00:22,889 --> 00:00:26,121 it's actually defined for any real number that you stick there for x 10 00:00:26,121 --> 00:00:28,239 so, when we talk about sampling the domain, 11 00:00:28,239 --> 00:00:30,639 we can actually pick any real number for x 12 00:00:30,639 --> 00:00:35,057 I'm actually going to pick real numbers that are fairly small in magnitude 13 00:00:35,057 --> 00:00:36,405 so that they're easy to graph, 14 00:00:36,405 --> 00:00:40,136 so you don't have to plot, you know, 8 billion on a number line over here. 15 00:00:40,152 --> 00:00:44,072 So let's draw ourselves some simple graph paper, 16 00:00:44,072 --> 00:00:46,140 let's call that the x-axis 17 00:00:46,140 --> 00:00:49,372 let's call that the y-axis 18 00:00:49,372 --> 00:00:52,639 or actually I should call it the y=f(x) 19 00:00:52,639 --> 00:00:56,695 so whatever my x is, I input it into this function definition, 20 00:00:56,706 --> 00:01:00,190 it'll tell me what the function value is there, it'll tell me f(x), 21 00:01:00,190 --> 00:01:02,156 and we're going to say that y is equal to that. 22 00:01:02,156 --> 00:01:06,671 Let's draw a little table here to try out some values. 23 00:01:06,671 --> 00:01:10,473 So, let's say that this is x values and this is f(x) 24 00:01:10,488 --> 00:01:16,512 and I can even say that these are my y values which are going to be equal to f(x). 25 00:01:16,512 --> 00:01:20,057 So let's start with, I'm going to try, 26 00:01:20,057 --> 00:01:27,906 -2, -1, 0, 1, and 2. 27 00:01:27,906 --> 00:01:30,172 So let's try -2 first. 28 00:01:30,172 --> 00:01:34,307 If x is equal to -2, what is f(x)? 29 00:01:34,307 --> 00:01:37,724 Well f(x) is going to 5 times -2 minus 4, 30 00:01:37,724 --> 00:01:41,755 so it's 5 times -2 minus 4 31 00:01:41,755 --> 00:01:47,256 which is equal to -10 minus 4, which is -14 32 00:01:47,256 --> 00:01:49,589 So let me plot that over here, 33 00:01:49,589 --> 00:01:53,474 I'm going to have a slightly more scrunched up scale 34 00:01:53,477 --> 00:01:56,664 on the y-axis, and actually, let me give myself some space 35 00:01:56,664 --> 00:01:58,206 so I can go further down 36 00:01:58,206 --> 00:02:01,871 let me clear this, give myself a little bit of space 37 00:02:01,871 --> 00:02:03,630 'cause I'm feeling I'll be using a lot of 38 00:02:03,630 --> 00:02:07,360 negative values since I just got all the way down to -14 39 00:02:07,372 --> 00:02:11,780 so let me go further down here and then let me mark off some increments over here. 40 00:02:11,780 --> 00:02:15,989 So let's say that this is -5, 41 00:02:15,989 --> 00:02:17,956 this is -10, 42 00:02:17,956 --> 00:02:21,322 and this is -15, 43 00:02:21,322 --> 00:02:25,058 and then this would be +5, 44 00:02:25,058 --> 00:02:27,672 and this would be +10. 45 00:02:27,672 --> 00:02:30,390 So, when x is -2, 46 00:02:30,390 --> 00:02:39,233 f(x) is equal to -14 47 00:02:39,233 --> 00:02:44,005 which is right about there, so that is -14 48 00:02:44,005 --> 00:02:47,356 so that right over there is the point (-2, -14) 49 00:02:47,356 --> 00:02:49,956 which we got right from that 50 00:02:49,956 --> 00:02:53,748 Now let's try another point. Let's try -1. 51 00:02:53,773 --> 00:02:55,922 When x is -1, f(x) is 52 00:02:55,922 --> 00:02:59,322 5 times -1 minus 4 53 00:02:59,322 --> 00:03:01,840 5 times -1 is -5, 54 00:03:01,840 --> 00:03:04,725 minus 4 is -9. 55 00:03:04,725 --> 00:03:07,622 So when x is -1, 56 00:03:07,622 --> 00:03:10,057 f(x) is -9. 57 00:03:10,057 --> 00:03:13,673 So -9 is right about here. 58 00:03:13,673 --> 00:03:18,620 So this is -9, so this is the point (-1, -9). 59 00:03:18,620 --> 00:03:22,690 That is on the graph of f(x). 60 00:03:22,690 --> 00:03:26,854 And now let's try zero. When x is 0, f(x) is going to be 61 00:03:26,856 --> 00:03:30,407 5 times 0 minus 4 62 00:03:30,407 --> 00:03:34,507 Well that's just 0 minus 4 which is equal to -4, 63 00:03:34,523 --> 00:03:38,823 So when x is 0, f(x) is equal to -4. 64 00:03:38,823 --> 00:03:40,656 That's -4 right over there 65 00:03:40,656 --> 00:03:44,687 and actually, our point is going to be sitting right over there, that is 0, -4, 66 00:03:44,706 --> 00:03:46,407 we're to the left of the point. 67 00:03:46,407 --> 00:03:49,918 Let's keep going! Let's see what happens when x is equal to 1. 68 00:03:49,923 --> 00:03:56,209 When x is equal to 1, f(x) is equal to 5 times 1 minus 4. 69 00:03:56,257 --> 00:04:00,969 5 times 1 is 5, minus 4 is equal to 1. 70 00:04:00,990 --> 00:04:05,661 So we get to the point (1,1), which is right about there 71 00:04:05,673 --> 00:04:08,573 so this is point (1,1). 72 00:04:08,573 --> 00:04:14,177 and then let's just try one more. Let's see what happens when x is equal to 2. 73 00:04:14,191 --> 00:04:19,129 Then f(x) is 5 times 2 minus 4, 74 00:04:19,129 --> 00:04:23,687 which is 10 minus 4, which is equal to 6. 75 00:04:23,687 --> 00:04:28,544 So, we have when x is equal to 2, f(x) is equal to 6. 76 00:04:28,544 --> 00:04:30,924 So that's right about there. 77 00:04:30,924 --> 00:04:35,901 That's 6 right there, so this is the point (2, 6). 78 00:04:35,924 --> 00:04:39,408 So once again, these are just sample points from the domain, 79 00:04:39,423 --> 00:04:42,635 this isn't the entire domain, but it gives us enough points 80 00:04:42,635 --> 00:04:46,066 to see the general structure of the graph. 81 00:04:46,066 --> 00:04:50,356 If we connect the dots, we see a line forming. 82 00:04:50,356 --> 00:04:53,920 If we connect the dots, it looks something like this, 83 00:04:53,920 --> 00:04:57,236 and my shaky hand makes it look a little bit curvy, but 84 00:04:57,239 --> 00:04:59,440 it should be an absolute straight line. 85 00:04:59,440 --> 00:05:02,100 If I had this on really good graph paper, 86 00:05:02,107 --> 00:05:04,504 and if I had a ruler, you'd see that this is a straight line 87 00:05:04,504 --> 00:05:06,479 and it would keep going on and on and on 88 00:05:06,479 --> 00:05:09,440 And I want to make it clear that we just sampled points from the domain, 89 00:05:09,440 --> 00:05:10,923 but we can take any point 90 00:05:10,923 --> 00:05:12,357 in the domain, which we already said 91 00:05:12,357 --> 00:05:13,758 is all real numbers, 92 00:05:13,758 --> 00:05:16,173 so if we took right over here, 93 00:05:16,173 --> 00:05:17,408 we said 1.5, 94 00:05:17,408 --> 00:05:17,991 you could see, 95 00:05:17,991 --> 00:05:19,357 and if you graph 1.5, 96 00:05:19,357 --> 00:05:20,324 f(1.5) should sit 97 00:05:20,324 --> 00:05:21,858 on that line right over there. 98 00:05:21,858 --> 00:05:23,791 If you graph f(-.5), 99 00:05:23,791 --> 00:05:25,441 so this is -.5, 100 00:05:25,441 --> 00:05:27,357 if you graphed f(-.5), 101 00:05:27,357 --> 00:05:30,090 it should sit on the line right over there. 102 00:05:30,090 --> 00:05:30,990 But we're done! 103 00:05:30,990 --> 00:05:32,790 We have graphed the function 104 00:05:32,790 --> 99:59:59,999 f(x)=5x-4.