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Popular >

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 3

Y Intercepts : (0, sin (3 \cdot 0) + 2)

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [1, 3]

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 3

Axis interception points of

sin (3 x) + 2 :

Y Intercepts

: (0, sin (3 \cdot 0) + 2)

Asymptotes of

sin (3 x) + 2 :

None

Extreme Points of

sin (3 x) + 2 :

Maximum

(\frac{π}{6} + \frac{2 π}{3} n, 3),

Minimum

(\frac{π}{2} + \frac{2 π}{3} n, 1)

Popular Examples

y = \frac{4}{3} x + 1

f (n) = 8 + 27 n^{3}

f (x) = (1 - 2 x)^{3}

f (t) = - 16 t^{2}

y = - 9 x^{2}

Frequently Asked Questions (FAQ)

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