Using technology to graph and evaluate functions

0:00- [Instructor] What we're gonna do in this video is get a little bit of practice using a graphing tool. In this case, I'm using Desmos as my graphing calculator, and you might already have experience that you could graph a function. So it's gonna graph y equals f of x, but we're defining f of x to be 8x plus 15.

0:16So this is going to be a line here that's interesting, and notice I can scan along this line and I can see different points that are on that line. But what I'm curious about is evaluating it at a given x value, and the x value I care about is 3.25, so I wanna figure out, what is f of 3.25?

0:36So one way I could do it is just scan along this line, and notice I go off the screen. So maybe I wanna zoom in, actually zoom out a little bit. So 3.25's around here, so I'm gonna be going, actually, I'm gonna be going even higher than that. So if I just keep scanning this, when x is equal to 3.25, y, or f of x is equal to 41, so that's one way to do it.

1:02A slightly cleaner way of doing it is I could say, okay, let me just graph the vertical line x. Whoops, x equals 3.25. And what's nice about that is Desmos will actually show us the point of intersection, so it says it very clearly there. When x is equal to 3.25, y equals f of x is equal to 41.

1:25Now, Desmos also has a very convenient thing where you could literally just say f of 3.25 and, whoops, not 3.5, f of 3.25. 3.25, and it just calculated it being 41. My guess is how it does it is it is actually just substituting in for the original equation, which is what I would do if I were just doing this on pencil and paper and I didn't have a grapher here.

1:51I would just say, whoa, eight times 3.25 plus 15 is equal to 41. Now let's go the other way. Let's think about if we wanna say at what x value does our function hit a certain value? And in this case, let's say, at what x value does our function hit 36.6? And I just picked that number arbitrarily, so we could do the same thing.

2:12Okay, let's see when our y value is 36.6. 36.6 is right, I just saw it, there you go. At x equals 2.7, y is equal to 36.6, so you could do it that way. You could also just graph another line. You could say y is equal to 36 point, or I should say is equal to, yes, 36.6.

2:40And you could see the point of intersection right over there, x is 2.7. Now, of course, you can always just do it algebraically. In that last example, you could just try to solve the equation, 36.6 is equal to 8x plus 15 and you would get the same result.