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Popular Calculus >

f(x)=2sec(x)

Solution

f (x) = 2 sec (x)

Solution

Period : 2 π

Domain : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

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

Y Intercepts : (0, 2)

Asymptotes : Vertical x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Extreme Points : Minimum (2 πn, 2), Maximum (π + 2 πn, - 2)

+1

Interval Notation

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

Solution steps

Periodicity of

2 sec (x) : 2 π

Domain of

2 sec (x) : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range of

2 sec (x) : f (x) \leq - 2 or f (x) \geq 2

Axis interception points of

2 sec (x) :

Y Intercepts

: (0, 2)

Asymptotes of

2 sec (x) :

Vertical

: x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Extreme Points of

2 sec (x) :

Minimum

(2 πn, 2),

Maximum

(π + 2 πn, - 2)

Graph

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