Determine the point(s), if any, at which the function is discontinuous and state the type of discontinuity. f(x)= {x^2+3 x2 ( this symbol-{ is supposed to one big { )

Question

Determine the point(s), if any, at which the function is discontinuous and state the type of discontinuity.

f(x)= {x^2+3      x<1
         {10-x        1≤x≤2
         {6x-x^2     x>2

( this symbol->{ is supposed to one big {  )

anonymous · Answer

replace $x$ by $1$ in the top two expressions
if the answers are the same, then it is continuous
if not, then it is not
repeat for the bottom two with $x=2$

anonymous · Answer

so what if the top 2 expressions are not the same if x=1 but the bottom two are the same if x=2? Is it discontinuous or continuous? because isn't this one function?

anonymous · Answer

it is one function, it is one piecewise functions (most are) but if the top two are not the same at 1, then it is discontinuous at 1, and if the bottom two are the same at 2, then it is continuous at 2

anonymous · Answer

your answer should be "discontinuous at $x=1$"

anonymous · Answer

ah ok, I see. that makes sense with a similar graph in my book

anonymous · Answer

btw the type of discontinuity is "jump" which you will see if you graph it

anonymous · Answer

not that you have to graph it, it does not go to infinity at 1, just jumps

anonymous · Answer

ah ok, btw is there such a thing as "infinite" discontinuity?