Question

Determine for what numbers, if any, the given function is discontinuous.

f(x) = {x-5 if x is less than or equal to 5
x^2-10 if x is greater than 5}

Answer 1

try doing this
\[\lim_{x \rightarrow 5-} f(x)\]
and
\[\lim_{x \rightarrow 5+} f(x)\]

if they are not equal then the function is discontinuous at that point

Answer 2

do you understand?

Answer 3

Would the answer be 0?

Answer 4

so lets look at the limit as x approaches 5 from the left
all you do is substitute it in the first equation
5 - 5 = 0

now you look at it from the right side
so you just plug it in the 2nd equation since its a little bit bigger than 5

Answer 5

then you compare the 2 answers together and you shown that as you approach 5 from both directions you converge into 2 different values which causes the function to become dicontinuous

Answer 6

does that make sense?

Answer 7

I think so...
Here are my choices:
A. 5
B. None
C. 0
D. -5, 5

Answer 8

I know the answer isn't D...

Answer 9

its 5, A

Answer 10

it helps to draw it out
once you graph it you can see the line gets diconnected at x=5

Answer 11

Thank you!

Answer 12

your welcome