Ex 2: Graphing a basic function Graphing a Basic Function
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- We're asked to graph the function f(x)=5x-4
- and we'll do it by really just sampling some points from the domain
- and seeing what value our function takes
- and then we'll just graph those points
- and then we'll just connect the dots and see what forms,
- and there's other ways to do this
- but this is kind of the most simple, or the most basic way.
- So if you look at this function over here,
- it's actually defined for any real number that you stick there for x
- so, when we talk about sampling the domain,
- we can actually pick any real number for x
- I'm actually going to pick real numbers that are fairly small in magnitude
- so that they're easy to graph,
- so you don't have to plot, you know, 8 billion on a number line over here.
- So let's draw ourselves some simple graph paper,
- let's call that the x-axis
- let's call that the y-axis
- or actually I should call it the y=f(x)
- so whatever my x is, I input it into this function definition,
- it'll tell me what the function value is there, it'll tell me f(x),
- and we're going to say that y is equal to that.
- Let's draw a little table here to try out some values.
- So, let's say that this is x values and this is f(x)
- and I can even say that these are my y values which are going to be equal to f(x).
- So let's start with, I'm going to try,
- -2, -1, 0, 1, and 2.
- So let's try -2 first.
- If x is equal to -2, what is f(x)?
- Well f(x) is going to 5 times -2 minus 4,
- so it's 5 times -2 minus 4
- which is equal to -10 minus 4, which is -14
- So let me plot that over here,
- I'm going to have a slightly more scrunched up scale
- on the y-axis, and actually, let me give myself some space
- so I can go further down
- let me clear this, give myself a little bit of space
- 'cause I'm feeling I'll be using a lot of
- negative values since I just got all the way down to -14
- so let me go further down here and then let me mark off some increments over here.
- So let's say that this is -5,
- this is -10,
- and this is -15,
- and then this would be +5,
- and this would be +10.
- So, when x is -2,
- f(x) is equal to -14
- which is right about there, so that is -14
- so that right over there is the point (-2, -14)
- which we got right from that
- Now let's try another point. Let's try -1.
- When x is -1, f(x) is
- 5 times -1 minus 4
- 5 times -1 is -5,
- minus 4 is -9.
- So when x is -1,
- f(x) is -9.
- So -9 is right about here.
- So this is -9, so this is the point (-1, -9).
- That is on the graph of f(x).
- And now let's try zero. When x is 0, f(x) is going to be
- 5 times 0 minus 4
- Well that's just 0 minus 4 which is equal to -4,
- So when x is 0, f(x) is equal to -4.
- That's -4 right over there
- and actually, our point is going to be sitting right over there, that is 0, -4,
- we're to the left of the point.
- Let's keep going! Let's see what happens when x is equal to 1.
- When x is equal to 1, f(x) is equal to 5 times 1 minus 4.
- 5 times 1 is 5, minus 4 is equal to 1.
- So we get to the point (1,1), which is right about there
- so this is point (1,1).
- and then let's just try one more. Let's see what happens when x is equal to 2.
- Then f(x) is 5 times 2 minus 4,
- which is 10 minus 4, which is equal to 6.
- So, we have when x is equal to 2, f(x) is equal to 6.
- So that's right about there.
- That's 6 right there, so this is the point (2, 6).
- So once again, these are just sample points from the domain,
- this isn't the entire domain, but it gives us enough points
- to see the general structure of the graph.
- If we connect the dots, we see a line forming.
- If we connect the dots, it looks something like this,
- and my shaky hand makes it look a little bit curvy, but
- it should be an absolute straight line.
- If I had this on really good graph paper,
- and if I had a ruler, you'd see that this is a straight line
- and it would keep going on and on and on
- And I want to make it clear that we just sampled points from the domain,
- but we can take any point
- in the domain, which we already said
- is all real numbers,
- so if we took right over here,
- we said 1.5,
- you could see,
- and if you graph 1.5,
- f(1.5) should sit
- on that line right over there.
- If you graph f(-.5),
- so this is -.5,
- if you graphed f(-.5),
- it should sit on the line right over there.
- But we're done!
- We have graphed the function
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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