Limit and Continuity of a Piecewise Function

Question

Let $$f$$ be the function defined by $$f(x)=\begin{cases} x^2 & x<3 \ 2x+1 & x\ge3 \end{cases}$$. Consider the following statements.

I. The limit of $$f(x)$$ as $$x$$ approaches $$3$$ is $$9$$.
II. For a function to be continuous at $$x=3$$, its limit as $$x$$ approaches $$3$$ must equal its value at $$x=3$$.
III. The function $$f$$ is discontinuous at $$x=3$$ because its left-hand limit is $$9$$, whereas $$f(3)=7$$.

Which of the above statements is or are true?

Accepted Answer

II and III are true

Answer

I and III are true

Answer

Only I is true

Answer

All three are true

Rank	User	Correct Count	Attempt Count	Total Time	Score
#1	manya10rm	1	1	0m 00s	100
#2	bellabriceno89	1	1	0m 46s	54
#3	lesleiman	1	1	1m 15s	25

Limit and Continuity of a Piecewise Function

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