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Popular >

f(x)=(sin(3x))/3

Solution

f (x) = \frac{sin ( 3 x )}{3}

Solution

Period : \frac{2 π}{3}

Domain : - \infty < x < \infty

Range : - \frac{1}{3} \leq f (x) \leq \frac{1}{3}

X Intercepts : (\frac{2 πn}{3}, 0), (\frac{π}{3} + \frac{2 πn}{3}, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Maximum (\frac{π}{6} + \frac{2 π}{3} n, \frac{1}{3}), Minimum (\frac{π}{2} + \frac{2 π}{3} n, - \frac{1}{3})

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Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1}{3}, \frac{1}{3}]

Solution steps

Periodicity of

\frac{sin ( 3 x )}{3} : \frac{2 π}{3}

Domain of

\frac{sin ( 3 x )}{3} : - \infty < x < \infty

Range of

\frac{sin ( 3 x )}{3} : - \frac{1}{3} \leq f (x) \leq \frac{1}{3}

Axis interception points of

\frac{sin ( 3 x )}{3} :

X Intercepts

: (\frac{2 πn}{3}, 0), (\frac{π}{3} + \frac{2 πn}{3}, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{sin ( 3 x )}{3} :

None

Extreme Points of

\frac{sin ( 3 x )}{3} :

Maximum

(\frac{π}{6} + \frac{2 π}{3} n, \frac{1}{3}),

Minimum

(\frac{π}{2} + \frac{2 π}{3} n, - \frac{1}{3})

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Frequently Asked Questions (FAQ)

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