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Popular Calculus >

f(x)=sin(3x+2)

Solution

f (x) = sin (3 x + 2)

Solution

Period : \frac{2 π}{3}

Domain : - \infty < x < \infty

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

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

Asymptotes : None

Extreme Points : Minimum (- \frac{2}{3} + \frac{π}{2} + \frac{2 π}{3} n, - 1), Maximum (\frac{- 4 + 5 π}{6} + \frac{2 π}{3} n, 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 1]

Solution steps

Periodicity of

sin (3 x + 2) : \frac{2 π}{3}

Domain of

sin (3 x + 2) : - \infty < x < \infty

Range of

sin (3 x + 2) : - 1 \leq f (x) \leq 1

Axis interception points of

sin (3 x + 2) :

X Intercepts

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

Y Intercepts

: (0, sin (2))

Asymptotes of

sin (3 x + 2) :

None

Extreme Points of

sin (3 x + 2) :

Minimum

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

Maximum

(\frac{- 4 + 5 π}{6} + \frac{2 π}{3} n, 1)

Graph

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