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Popular >

f(x)=3csc(x)

Solution

f (x) = 3 csc (x)

Solution

Period : 2 π

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

Range : f (x) \leq - 3 or f (x) \geq 3

Intercepts : None

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

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

+1

Interval Notation

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

Range : (- \infty, - 3] \cup [3, \infty)

Solution steps

Periodicity of

3 csc (x) : 2 π

Domain of

3 csc (x) : 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range of

3 csc (x) : f (x) \leq - 3 or f (x) \geq 3

Axis interception points of

3 csc (x) :

None

Asymptotes of

3 csc (x) :

Vertical

: x = 2 πn, x = π + 2 πn

Extreme Points of

3 csc (x) :

Minimum

(\frac{π}{2} + 2 πn, 3),

Maximum

(\frac{3 π}{2} + 2 πn, - 3)

Popular Examples

f(x)=(3-e^{-2x})^5

f (x) = (3 - e^{- 2 x})^{5}

p(x)=2x^3+7x^2+2x-3

p (x) = 2 x^{3} + 7 x^{2} + 2 x - 3

f(x)=(x+2)/((x+4)(x+1))

f (x) = \frac{x + 2}{( x + 4 ) ( x + 1 )}

y=(2x+1)^5(x^3-x+1)^4

y = (2 x + 1)^{5} (x^{3} - x + 1)^{4}

y = ∣ x - 2 ∣, - 1 < x < 5

Frequently Asked Questions (FAQ)

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