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Popular Functions >

y=sin^4(2x+3)

Solution

y = sin^{4} (2 x + 3)

Solution

Period : \frac{π}{2}

Domain : - \infty < x < \infty

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

X Intercepts : (- \frac{3}{2} + \frac{π}{2} + \frac{πn}{2}, 0), (\frac{π}{2} - \frac{3}{2} + \frac{πn}{2}, 0), Y Intercepts : (0, sin^{4} (2 \cdot 0 + 3))

Asymptotes : None

Extreme Points : Minimum (\frac{- 3 + π}{2} + \frac{π}{2} n, 0), Minimum (\frac{π}{2} - \frac{3}{2} + \frac{π}{2} n, 0), Maximum (\frac{- 6 + 3 π}{4} + \frac{π}{2} n, 1), Maximum (- \frac{3}{2} + \frac{3 π}{4} + \frac{π}{2} n, 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [0, 1]

Solution steps

Periodicity of

sin^{4} (2 x + 3) : \frac{π}{2}

Domain of

sin^{4} (2 x + 3) : - \infty < x < \infty

Range of

sin^{4} (2 x + 3) : 0 \leq f (x) \leq 1

Axis interception points of

sin^{4} (2 x + 3) :

X Intercepts

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

Y Intercepts

: (0, sin^{4} (2 \cdot 0 + 3))

Asymptotes of

sin^{4} (2 x + 3) :

None

Extreme Points of

sin^{4} (2 x + 3) :

Minimum

(\frac{- 3 + π}{2} + \frac{π}{2} n, 0),

Minimum

(\frac{π}{2} - \frac{3}{2} + \frac{π}{2} n, 0),

Maximum

(\frac{- 6 + 3 π}{4} + \frac{π}{2} n, 1),

Maximum

(- \frac{3}{2} + \frac{3 π}{4} + \frac{π}{2} n, 1)

Graph

Popular Examples

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f(x)=\sqrt[3]{x+3}-2

Frequently Asked Questions (FAQ)

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