Question

I don't understand how to graph this step function? Question is in the comments.

Answer 1

\[f(x) = 2 \times \lceil x \rceil \] for the domain \[-2 < x \le 1\]

Answer 2

Let me look up the notation again, I always get ceiling and floor confused. :)

Answer 3

Okay, thanks :)

Answer 4

My understanding is that this is the ceiling function, you can think of it as the "round-up" function.

Answer 5

So, this means that if we have \[\lceil 0.4 \rceil = 1\] the result rounds to 1

Answer 6

of course, an extreme case is when \[\lceil -1.4 \rceil = -1\] which is kind of weird since "up" is "down" in negative land... Think of "up" as "more positive". :) Make sense so far as to how the ceiling function works?

Answer 7

Yeah, I do understand how the ceiling function works, but what confuses me is how to even begin graphing it. Graphing is definitely not my forte

Answer 8

OK, that shouldn't be too bad.

Answer 9

We only need to graph from -2 < x <=1.

Answer 10

Let's start with the right side of the graph. When x = 1. Then we have 2*ceiling(1), which rounds to 2*1 = 2.

Answer 11

The graph looks like this.

Answer 12

See? The x = 1, and the y = 2. Is that ok?

Answer 13

Remember that f(x) creates the y value. :)

Answer 14

We aren't done yet, there is more, but this is our first step.

Answer 15

Oh okay, I think it's starting to make sense. So to make the graph am I just plugging in values that are between -2 and 1? Including 1 as a value because of the less than or equal to sign?

Answer 16

Yes, that is the idea. You can plot an "open dot" for x = -2 just for a reference if it helps.

Answer 17

Would you like to see the rest of the graph? Or do you want to try it on your own first and then check?

Answer 18

I wanna try it and then have you check, if that's alright :)

Answer 19

Fine with me. That's the best way to learn! Let me know when you have it. :)

Answer 20

I'll attach what I got to this message, just so you have it.

Answer 21

Message if you have any questions! Good work and good luck! :)

Answer 22

@jtvatsim I ended up getting the same graph as yours! Thank you so much!

Answer 23

Excellent good job, you earn a medal! :)