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Popular >

f(x)= 2/3 cos(4x+(8pi)/3)

Solution

f (x) = \frac{2}{3} cos (4 x + \frac{8 π}{3})

Solution

Period : \frac{π}{2}

Domain : - \infty < x < \infty

Range : - \frac{2}{3} \leq f (x) \leq \frac{2}{3}

X Intercepts : (\frac{11 π}{24} + \frac{πn}{2}, 0), (\frac{5 π}{24} + \frac{πn}{2}, 0), Y Intercepts : (0, - \frac{1}{3})

Asymptotes : None

Extreme Points : Minimum (\frac{π}{12} + \frac{π}{2} n, - \frac{2}{3}), Maximum (\frac{π}{3} + \frac{π}{2} n, \frac{2}{3})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{2}{3}, \frac{2}{3}]

Solution steps

Periodicity of

\frac{2}{3} cos (4 x + \frac{8 π}{3}) : \frac{π}{2}

Domain of

\frac{2}{3} cos (4 x + \frac{8 π}{3}) : - \infty < x < \infty

Range of

\frac{2}{3} cos (4 x + \frac{8 π}{3}) : - \frac{2}{3} \leq f (x) \leq \frac{2}{3}

Axis interception points of

\frac{2}{3} cos (4 x + \frac{8 π}{3}) :

X Intercepts

: (\frac{11 π}{24} + \frac{πn}{2}, 0), (\frac{5 π}{24} + \frac{πn}{2}, 0),

Y Intercepts

: (0, - \frac{1}{3})

Asymptotes of

\frac{2}{3} cos (4 x + \frac{8 π}{3}) :

None

Extreme Points of

\frac{2}{3} cos (4 x + \frac{8 π}{3}) :

Minimum

(\frac{π}{12} + \frac{π}{2} n, - \frac{2}{3}),

Maximum

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

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Frequently Asked Questions (FAQ)

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