Consider the following. f ( x ) = Describe the interval(s) on which the function
ID: 2855737 • Letter: C
Question
Consider the following.
f(x) =
Describe the interval(s) on which the function is continuous. (Enter your answer using interval notation.)
Identify any discontinuities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
x =
If the function has any discontinuities, identify the conditions of continuity that are not satisfied. (Select all that apply. Select each choice if it is met for any of the discontinuities.)
A.
There is a discontinuity at x = c where f(c) is not defined.
B.
There is a discontinuity at x = c where lim xc f(x) f(c).
C.
There is a discontinuity at x = c where lim xc f(x) does not exist.
D.
There are no discontinuities; f(x) is continuous.
Explanation / Answer
For the function f(x) to be continuous at x = c
lim [x -> c-] f(x) = lim [x -> c+] f(x) = f(c)
both 5 +x , x2 +3 are continuous functions
Checking continuity at x = 2
==> lim [x -> 2-] f(x) = lim [x -> 2-] 5 + x since for values less than 2 , f(x) = 5 +x
==> 5 + 2 = 7
==> lim [x -> 2+] f(x) = lim [x -> 2+] x2 + 3 since for values greater than 2 , f(x) = x2 +3
==> 22 + 3 = 7
f(2) = 5 + 2 = 7 since at x = 2 , f(x) = x +5
as lim [x -> 2-] f(x) = lim [x -> 2+] f(x) = f(c)
function is continuous at every x
Discontinuity does not exist