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Popular Functions >

f(x)= 4/(sin(x))+2

Solution

f (x) = \frac{4}{sin ( x )} + 2

Solution

Period : 2 π

Domain : 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range : f (x) \leq - 2 or f (x) \geq 6

Intercepts : None

Asymptotes : Vertical x = 2 πn, x = π + 2 πn

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

+1

Interval Notation

Domain : (2 πn, π + 2 πn) \cup (π + 2 πn, 2 π + 2 πn)

Range : (- \infty, - 2] \cup [6, \infty)

Solution steps

Periodicity of

\frac{4}{sin ( x )} + 2 : 2 π

Domain of

\frac{4}{sin ( x )} + 2 : 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range of

\frac{4}{sin ( x )} + 2 : f (x) \leq - 2 or f (x) \geq 6

Axis interception points of

\frac{4}{sin ( x )} + 2 :

None

Asymptotes of

\frac{4}{sin ( x )} + 2 :

Vertical

: x = 2 πn, x = π + 2 πn

Extreme Points of

\frac{4}{sin ( x )} + 2 :

Minimum

(\frac{π}{2} + 2 πn, 6),

Maximum

(\frac{3 π}{2} + 2 πn, - 2)

Graph

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Frequently Asked Questions (FAQ)

What is the f(x)= 4/(sin(x))+2 ?
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