Continuity - Find the intervals on which each function is continuous

Q: What are the main instructions for the worksheet?

Find the intervals on which each function is continuous, and use the provided graphs to sketch the functions when needed.

Q: Do the problems include piecewise functions?

Yes. Several questions define f(x) in different forms depending on x, requiring interval-based continuity checking.

Q: What should be done when a function is not continuous?

Locate the x-axis location(s) of the discontinuity and classify each discontinuity type.

Oct 8, 2026

Uploaded by Alex Sinclair

Worksheet for Infinite Calculus focused on determining continuity of piecewise and multi-form functions. Tasks require finding the intervals where each given function remains continuous, with optional use of provided graphs to sketch behavior around breakpoints. The problems include multiple numbered functions, including piecewise definitions and composite expressions, followed by additional critical thinking items that ask students to assess whether functions are continuous everywhere, identify discontinuity locations, and classify discontinuity types.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Find intervals of continuity

Piecewise functions and graphs

Determine continuity and classify discontinuities

Critical thinking questions

Kuta Software-Infinite Calculus Name Continuity Date Period Find the intervals on which each function is continuous. x 2 + 2x + 1, x < 1 1) f (x) = {− ~~ ~~x~~ ~~ , x ≥ 1 2 2) f (x) = {13,, xx 55 | | | | f | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | 10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 6 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | − | 2 | | | 2 | | 4 | | 6 | | | 8 | 1 | 0 | 1 | 2 | x | | | | | | | | | | | | | | | | | | | | | | −2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | −4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | −6 | | | | | | | | | | | | | | | | Find the intervals on which each function is continuous. You may use the provided graph to sketch the function. 3) f (x) = {20x, − 10, xx 22 | | | | | | | f | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | | | | | | | | | | | | | | | | | | | 4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | −6 | − | 4 | − | 2 | | | 2 | | 4 | | 6 | | | 8 | 1 | 0 x | | | | | | | | | | | | | | | | | | | | | | | | | −2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | −4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | −6 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | −8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | − | 10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 4) f ( x) = ~~ ~~x2~~ ~~~~ ~~−1~~ ~~2~~ ~~ | | | | | | | | | | f | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | | | | | | | | | | | | | | | | | | | | | | 4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | − | 8 | − | 6 | − | 4 | − | 2 | | | 2 | | 4 | | 6 | | x | | | | | | | | | | | | | | | | | | | | | | | | | | | | −2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | −4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | −6 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | −8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | − | 10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Find the intervals on which each function is continuous. 5) f ( x) = ~~ ~~2xx~~ ~~4~~ ~~ 6) f (x) = {−x2x2 722x, − 2, xx 00 7) f (x) = − ~~ ~~x~~ ~~2~~ ~~−x~~ ~~−3~~ ~~12~~ ~~ 8) f (x) = ~~ ~~x2~~ ~~~~ ~~6~~ ~~ Determine if each function is continuous. If the function is not continuous, find the x-axis location of and classify each disco

FAQs

What are the main instructions for the worksheet?

Find the intervals on which each function is continuous, and use the provided graphs to sketch the functions when needed.

Do the problems include piecewise functions?

Yes. Several questions define f(x) in different forms depending on x, requiring interval-based continuity checking.

What should be done when a function is not continuous?

Locate the x-axis location(s) of the discontinuity and classify each discontinuity type.

Oct 8, 2026

Uploaded by Alex Sinclair