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Popular >

y=sec(x+pi/4)

Solution

y = sec (x + \frac{π}{4})

Solution

Period : 2 π

Domain : 2 πn \leq x < \frac{π}{4} + 2 πn or \frac{π}{4} + 2 πn < x < \frac{5 π}{4} + 2 πn or \frac{5 π}{4} + 2 πn < x < 2 π + 2 πn

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

Y Intercepts : (0, 2)

Asymptotes : Vertical x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn

Extreme Points : Maximum (\frac{3 π}{4} + 2 πn, - 1), Minimum (\frac{7 π}{4} + 2 πn, 1)

+1

Interval Notation

Domain : [2 πn, \frac{π}{4} + 2 πn) \cup (\frac{π}{4} + 2 πn, \frac{5 π}{4} + 2 πn) \cup (\frac{5 π}{4} + 2 πn, 2 π + 2 πn)

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

Solution steps

Periodicity of

sec (x + \frac{π}{4}) : 2 π

Domain of

sec (x + \frac{π}{4}) : 2 πn \leq x < \frac{π}{4} + 2 πn or \frac{π}{4} + 2 πn < x < \frac{5 π}{4} + 2 πn or \frac{5 π}{4} + 2 πn < x < 2 π + 2 πn

Range of

sec (x + \frac{π}{4}) : f (x) \leq - 1 or f (x) \geq 1

Axis interception points of

sec (x + \frac{π}{4}) :

Y Intercepts

: (0, 2)

Asymptotes of

sec (x + \frac{π}{4}) :

Vertical

: x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn

Extreme Points of

sec (x + \frac{π}{4}) :

Maximum

(\frac{3 π}{4} + 2 πn, - 1),

Minimum

(\frac{7 π}{4} + 2 πn, 1)

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Frequently Asked Questions (FAQ)

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