Interpreting a piecewise function graph

0:00- [Instructor] So we have this interesting looking graph here, and we're told that it shows the price of a movie ticket in dollars as a function of a person's age in years. And what I want us to do is think about what this graph is telling us about how this theater charges people.

0:18So when you are just born, you're zero years old all the way through two years old, all the way up to, but not including, it looks like halfway between two and four, which is at three. So it looks at right at three years old, they start charging you. And how much do they start charging you?

0:36They are charging you $8 when you were three years old. So for example, if I had a one-year-old, if this is your age, let me write it this way, make a little table here. If you have your age, and then if you said this is the cost of the movie ticket, if your age is one-year-old, we're assuming this is in years, then you're gonna go for free.

1:00And actually that would be true anywhere from zero up to, but not including three years old. So if it's right before your third birthday, you could still get in for free. But right on your third birthday, officially, I don't know if your parents are gonna tell the truth, but officially, they would now charge you $8.

1:18So as soon as you turn three, you are going to be charged $8. And that's going to be true all the way until it looks like your 13th birthday. At your 13th birthday, it looks like there's another step up. And so if you're 13th plus, you are going to be charged $14 to get into that movie.

1:39And that's going to be no matter how old you are, above and beyond that. People will sometimes call this a piecewise-defined function. It's defined in pieces here. So you could say, all right, from zero up to, but not including three years old, it's free. From three years old up to, but not including 13, it's $8.

1:58And then from 13 all the way to however old you are, you're going to be paying $14 to see that movie.