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Popular >

f(x)=(1+sin(2x))/2

Solution

f (x) = \frac{1 + sin ( 2 x )}{2}

Solution

Period : π

Domain : - \infty < x < \infty

Range : 0 \leq f (x) \leq 1

X Intercepts : (\frac{3 π}{4} + πn, 0), Y Intercepts : (0, \frac{1}{2})

Asymptotes : None

Extreme Points : Maximum (\frac{π}{4} + πn, 1), Minimum (\frac{3 π}{4} + πn, 0)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [0, 1]

Solution steps

Periodicity of

\frac{1 + sin ( 2 x )}{2} : π

Domain of

\frac{1 + sin ( 2 x )}{2} : - \infty < x < \infty

Range of

\frac{1 + sin ( 2 x )}{2} : 0 \leq f (x) \leq 1

Axis interception points of

\frac{1 + sin ( 2 x )}{2} :

X Intercepts

: (\frac{3 π}{4} + πn, 0),

Y Intercepts

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

Asymptotes of

\frac{1 + sin ( 2 x )}{2} :

None

Extreme Points of

\frac{1 + sin ( 2 x )}{2} :

Maximum

(\frac{π}{4} + πn, 1),

Minimum

(\frac{3 π}{4} + πn, 0)

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Frequently Asked Questions (FAQ)

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