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How many intersections are there between the graphs of f(x) = 0.8x and g(x) = [x]?

 Mar 19, 2022
 #1
avatar+13900 
+1

There is only one touch point (0,0), no intersection point.

laugh  !

 Mar 19, 2022
 #3
avatar+13900 
+1

I thought that was abs(x). Please explain to us what the graph means. I didn't know anything like that before.

sad

asinus  Mar 20, 2022
edited by asinus  Mar 20, 2022
 #4
avatar+117872 
+1

Sorry asinus, I didn't see your question earlier.

[x] means nothing to me either.

I looked it up and it seems to be used sometimes in place of the floor function. \(\lfloor x\rfloor\)

I assume that this is because the floor function symbol is not on an ordinary keyboard and it is not a common symbol.

 

The floor function simply means 'round down' to the nearest integer.

 

so for example:

 

\(\lfloor 3 \rfloor =3\\ \lfloor 3.2 \rfloor =3\\ \lfloor 3.7 \rfloor =3\\ \lfloor 3.99999 \rfloor =3\\ \lfloor 4 \rfloor =4\\\)

Melody  Mar 20, 2022
 #5
avatar+13900 
+1

Thank you Melody! According to your information, I covered

f(x)= 0.8x with g(x)=ceil(x-1) in my graph program. I hadn't used ceil before.

There are three points of intersection and two points of contact.

Question: Do points of intersection and points of contact have the same designation in the English-speaking world?

laugh  !

asinus  Mar 20, 2022
 #6
avatar+117872 
+1

Yes, they are the same BUT they have to be included.

I made a mistake in my original answer.

The point (5,4) is NOT a point on the graph  y=floor of x   because the floor of 5 is 5 (not 4)

 

So there are only 4 points of intersection

 

Here is the correct graph

 

Melody  Mar 20, 2022
 #2
avatar+117872 
+1

Assuming that   [x] is a reference to the floor function,    which is normally written as  \(\lfloor x \rfloor\)

then there are 5

 

 Mar 20, 2022

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