Question

Why is the function f(x)=(1/2)x discontinuous

Answer 1

no. the answer says its discontinuous at even integers but the graph is just a straight line so i dont understand

Answer 2

\[f(x) = \frac 12 x\] is the equation of a straight line. It is continuous everywhere. The answer is wrong.

Answer 3

Can you post a screenshot of the question and where it says "discontinuous at even integers" ?

Answer 4

it claims to not be continuous at even numbers because:
lim (1/2)x=n
x->2n+


but
lim (1/2)x=n-1
x->2n-

Answer 5

Can you post a screenshot of the question. I think this is NOT f(x) = 1/2 * x.
You are omitting some information and a screenshot will help see what is being omitted in your question.

Answer 6

See, I knew it!!!

Answer 7

That is the greatest integer function as indicated by the square brackets around [1/2x].

Answer 8

I've never seen this before..

Answer 9

Ok now i understand it. Thank you so much

Answer 10

The greatest integer function f(x) = [x] is the greatest integer less than or equal to x.

Answer 11

f(x) = [x]
If x is an integer, then f(x) = x
If x is not an integer, then f(x) = the nearest integer to the LEFT of it.

Answer 12

[5] = 5
[149] = 149
[10.3] = 10
[-15.1] = -16
[5/4] = 1
[-5/4] = -2