Continuity

in what value of x does the following function is discontinuous?

• 3

• -3

• 6

• -6

Tags

CCSS.HSF-IF.C.7D

In what value of x will the following function discontinuous?

• -1

• -2

• -3

• -4

Tags

CCSS.HSF-IF.C.7D

A function is continuous on a number if and only if f(c) = lim f(x) as x approaches a number c.

• TRUE

• FALSE

One of the conditions a function must satisfy to be continuous at a number is "f(c) must exist"

• TRUE

• FALSE

Tags

CCSS.HSF.BF.B.3

A polynomial function is continuous to all real numbers.

• TRUE

• FALSE

The funciton f(x) = x²-2x+1, continuous to the interval [-7,7]

• TRUE

• FALSE

Tags

CCSS.HSF.IF.B.5

A piecewise function is continuous to any any interval.

• TRUE

• FALSE

Tags

CCSS.HSF-IF.C.7B

Is f(x) continuous at x = a, and why?

• No, $\lim_{x\rightarrow a^-}f\left(x\right)\ne\lim_{x\rightarrow a^+}f\left(x\right)$

• No, $\lim_{x\rightarrow a}f\left(x\right)\ne f\left(a\right)$

• Yes, $\lim_{x\rightarrow a^-}f\left(x\right)=\lim_{x\rightarrow a^+}f\left(x\right)$

• Yes, $\lim_{x\rightarrow a}f\left(x\right)=f\left(a\right)$

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Is the function continuous at x = 2, and why?

• Yes, $\lim_{x\rightarrow2}f\left(x\right)=f\left(2\right)$

• Yes, $\lim_{x\rightarrow2^-}f\left(x\right)=\lim_{x\rightarrow2^+}f\left(x\right)$

• No, $\lim_{x\rightarrow2^-}f\left(x\right)\ne\lim_{x\rightarrow2^+}f\left(x\right)$

• No, $\lim_{x\rightarrow2}f\left(x\right)\ne f\left(2\right)$

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

A function is continuous on a number if and only if f(c) = lim f(x) as x approaches a number c.

• TRUE

• FALSE