Question

Which graph represents the function over the interval [−3, 3]?

f(x)=⌈x⌉−3
Which graph represents the function over the interval [−3, 3]?

f(x)=⌈x⌉−3

Answer 1

I typed it twice on accident

Answer 2

can you screenshot the question? something seems off to me

Answer 3

Nothing is wrong , this is the question

Which graph represents the function over the interval [−3, 3]?

f(x)=⌈x⌉−3

Answer 4

wait, never mind, I read it wrong

Answer 5

I am on it

Answer 6

the -3 tells us the graph of the function is shifted 3 units down. so what then would be the answer?

Answer 7

i am not sure whst the brackets mean

Answer 8

oh, I got you now. This function is a greater integer function
What is Greatest Integer Function? The greatest integer function is a function that gives the largest integer which is less than or equal to x. This function is denoted by ⌊x⌋. We will round off the given number to the nearest integer that is less than or equal to the number itself.

Answer 9

what

Answer 10

ah, never mind, I will explain this differently:

Answer 11

the ticks mean floor or ceiling function, this is a ceiling function

Answer 12

I know the answer, but look at this link to see if you can figure it out: https://www.analyzemath.com/function/floor_function.html#:~:text=The%20floor%20function%20floor(x,the%20set%20of%20all%20integers.

Answer 13

They asked for what graph it is over the interval [-3,3], so use the given function: x-3=? to give you the answer. first plug in -3 and 3.
(-3)-3 = -6 so y must equal -6, 3-3=0, so y must equal 0.
the range of the correct function is (-6,0). when you have ceiling functions, every interval begins with an open dot, when you have floor functions, every interval begins with a closed dot

Answer 14

you should be able to get the answer now
\[\lceil x \rceil \lfloor x \rfloor\]the former means ceiling function, the latter means floor function. ceil. begins with open dot intervals, floor begins with closed dot intervals

Answer 15

yes, it should be the first one b