$$\delta (t) = \left\{ {\matrix{ {1,} & {t = 0} \cr {0,} & {otherwise} \cr } } \right.$$

$$\delta (t) = \left\{ {\matrix{ {\infty ,} & {t = 0} \cr {0,} & {otherwise} \cr } } \right.$$

$$\delta (t) = \left\{ {\matrix{ {1,} & {t = 0} \cr {0,} & {otherwise\,\,\,and\,\,\int\limits_{ - \infty }^\infty {\delta (t)\,dt = 1} } \cr } } \right.\,\,$$

$$\delta (t) = \left\{ {\matrix{ {\infty ,} & {t = 0} \cr {0,} & {otherwise\,\,\,and\,\,\int\limits_{ - \infty }^\infty {\delta (t)\,dt = 1} } \cr } } \right.\,\,$$

monotonically increases

monotonically decreases

increases to a maximum value and then decreases

decreases to a minimum value and then increases