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Popular >

y=2sin(1/3 x)

Solution

y = 2 sin (\frac{1}{3} x)

Solution

Period : 6 π

Domain : - \infty < x < \infty

Range : - 2 \leq f (x) \leq 2

X Intercepts : (6 πn, 0), (3 π + 6 πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Maximum (\frac{3 π}{2} + 6 πn, 2), Minimum (\frac{9 π}{2} + 6 πn, - 2)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 2, 2]

Solution steps

Periodicity of

2 sin (\frac{1}{3} x) : 6 π

Domain of

2 sin (\frac{1}{3} x) : - \infty < x < \infty

Range of

2 sin (\frac{1}{3} x) : - 2 \leq f (x) \leq 2

Axis interception points of

2 sin (\frac{1}{3} x) :

X Intercepts

: (6 πn, 0), (3 π + 6 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

2 sin (\frac{1}{3} x) :

None

Extreme Points of

2 sin (\frac{1}{3} x) :

Maximum

(\frac{3 π}{2} + 6 πn, 2),

Minimum

(\frac{9 π}{2} + 6 πn, - 2)

Popular Examples

f(x)=x^{1/((1-x))}

f (x) = x^{\frac{1}{( 1 - x )}}

y = 9 x + 6

f(x)=cosh(2x)-sinh(2x)

f (x) = cosh (2 x) - sinh (2 x)

y = x^{3} - 6

y = - 2 (x + 3) (x - 1)

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