Unknown parent function?

[mollyk]

I was able to fill out almost all the parent functions but I have two questions. My first question is what is the top middle graph? I’ve never seen, or maybe it’s just not ringing a bell, a graph before that breaks, or seems to break? My second question is my domain ans range for the greatest integer function correct? I think the range is wrong because it can’t contain non-integers but would that also mean the domain is wrong too? I’m not sure how I would have to write that in interval notation. I hope both of those make sense!

 

[lev888]

View attachment 28042View attachment 28043
I was able to fill out almost all the parent functions but I have two questions. My first question is what is the top middle graph? I’ve never seen, or maybe it’s just not ringing a bell, a graph before that breaks, or seems to break? My second question is my domain ans range for the greatest integer function correct? I think the range is wrong because it can’t contain non-integers but would that also mean the domain is wrong too? I’m not sure how I would have to write that in interval notation. I hope both of those make sense!

Look at x^(1/3) or similar for the top middle graph.
The range for [x] is the set of all integers (Z). Domain is correct.

 

[Dr.Peterson]

View attachment 28042View attachment 28043
I was able to fill out almost all the parent functions but I have two questions. My first question is what is the top middle graph? I’ve never seen, or maybe it’s just not ringing a bell, a graph before that breaks, or seems to break? My second question is my domain ans range for the greatest integer function correct? I think the range is wrong because it can’t contain non-integers but would that also mean the domain is wrong too? I’m not sure how I would have to write that in interval notation. I hope both of those make sense!

Not all domains and ranges can be written in interval notation, because not all sets are intervals! As you've been told (and as you yourself indicate) the range of the greatest integer function (also called the floor function) is the set of integers, which is just called \(\mathbb{Z}\).

The second function is the cube root (though any odd root looks similar); it doesn't literally break at zero, but it does momentarily become vertical.

 

[mollyk]

So it still would be a cube root function even though there’s a space/no line at the orgin? The “break” just represents becoming vertical?

 

[lev888]

So it still would be a cube root function even though there’s a space/no line at the orgin? The “break” just represents becoming vertical?

The break does look strange. I am assuming there is actually no break because a discontinuity should've been marked by circles, as in the greatest integer case.

Classification of discontinuities - Wikipedia

en.wikipedia.org