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Popular Calculus >

f(x)=sec(3x)

Solution

f (x) = sec (3 x)

Solution

Period : \frac{2 π}{3}

Domain : \frac{2 π}{3} n \leq x < \frac{π}{6} + \frac{2 π}{3} n or \frac{π}{6} + \frac{2 π}{3} n < x < \frac{π}{2} + \frac{2 π}{3} n or \frac{π}{2} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

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

Y Intercepts : (0, 1)

Asymptotes : Vertical x = \frac{π}{2} + \frac{2 π}{3} n, x = \frac{π}{6} + \frac{2 π}{3} n

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

+1

Interval Notation

Domain : [\frac{2 π}{3} n, \frac{π}{6} + \frac{2 π}{3} n) \cup (\frac{π}{6} + \frac{2 π}{3} n, \frac{π}{2} + \frac{2 π}{3} n) \cup (\frac{π}{2} + \frac{2 π}{3} n, \frac{2 π}{3} + \frac{2 π}{3} n)

Range : (- \infty, - 1] \cup [1, \infty)

Solution steps

Periodicity of

sec (3 x) : \frac{2 π}{3}

Domain of

sec (3 x) : \frac{2 π}{3} n \leq x < \frac{π}{6} + \frac{2 π}{3} n or \frac{π}{6} + \frac{2 π}{3} n < x < \frac{π}{2} + \frac{2 π}{3} n or \frac{π}{2} + \frac{2 π}{3} n < x < \frac{2 π}{3} + \frac{2 π}{3} n

Range of

sec (3 x) : f (x) \leq - 1 or f (x) \geq 1

Axis interception points of

sec (3 x) :

Y Intercepts

: (0, 1)

Asymptotes of

sec (3 x) :

Vertical

: x = \frac{π}{2} + \frac{2 π}{3} n, x = \frac{π}{6} + \frac{2 π}{3} n

Extreme Points of

sec (3 x) :

Minimum

(\frac{2 π}{3} n, 1),

Maximum

(\frac{π}{3} + \frac{2 π}{3} n, - 1)

Graph

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