Continuity of Graphed Functions

continuous

removable

non removable

Non removable Discontinuity

Removable Discontinuity

Continuous

Removable continuity

Continuous

Removable Discontinuity

Infinite Discontinuity

Jump Discontinuity

$x=-3$

$x=-6$

$x=1$

$x=2$

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

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

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

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

No, because f(a) is undefined

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, $\lim_{x\rightarrow2}f\left(x\right)\ne f\left(2\right)$

continuous at 2

non removable discontinuity at -1

removable discontinuity at -1

non removable discontinuity at 4

removable discontinuity at 4

continuous at -4

non removable discontinuity at -4

removable discontinuity at 0

removable discontinuity at -4

continuous at 0

continuous at -2

continuous at 1

removable discontinuity at -1

non removable discontinuity at 3

continuous at 4

continuous at -2

continuous at 1

removable discontinuity at 2

non removable discontinuity at 2

continuous at 2