What is the y= 1/(sqrt(2pi))e^{-(x^2)/2} ?

The y= 1/(sqrt(2pi))e^{-(x^2)/2} is

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y= 1/(sqrt(2pi))e^{-(x^2)/2}

y = \frac{1}{2 π} e^{- \frac{x ^{2}}{2}}

Domain : - \infty < x < \infty

Range : 0 < f (x) \leq \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

Y Intercepts : (0, \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}})

Asymptotes : Horizontal y = 0

Extreme Points : Maximum (0, \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}})

Interval Notation

Domain : (- \infty, \infty)

Range : (0, \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}]

Solution steps

Domain of

\frac{1}{2 π} e^{- \frac{x ^{2}}{2}} : - \infty < x < \infty

Range of

\frac{1}{2 π} e^{- \frac{x ^{2}}{2}} : 0 < f (x) \leq \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

Axis interception points of

\frac{1}{2 π} e^{- \frac{x ^{2}}{2}} :

Y Intercepts

: (0, \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}})

Asymptotes of

\frac{1}{2 π} e^{- \frac{x ^{2}}{2}} :

Horizontal

: y = 0

Extreme Points of

\frac{1}{2 π} e^{- \frac{x ^{2}}{2}} :

Maximum

(0, \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}})

f (a) = \frac{1}{a ^{3}}

y = \frac{16}{x}

f (x) = 7^{x + 1}

y = \frac{x + 4}{x ^{2} - 16}

y = ln (40000 - x^{2}) + sin (x^{100})