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Popular >

p(x)=(5+1)/(cos(x))

Solution

p (x) = \frac{5 + 1}{cos ( 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 - 6 or f (x) \geq 6

Y Intercepts : (0, 6)

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

Extreme Points : Minimum (2 πn, 6), Maximum (π + 2 πn, - 6)

+1

Interval Notation

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

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

Solution steps

Periodicity of

\frac{5 + 1}{cos ( x )} : 2 π

Domain of

\frac{5 + 1}{cos ( 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

\frac{5 + 1}{cos ( x )} : f (x) \leq - 6 or f (x) \geq 6

Axis interception points of

\frac{5 + 1}{cos ( x )} :

Y Intercepts

: (0, 6)

Asymptotes of

\frac{5 + 1}{cos ( x )} :

Vertical

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

Extreme Points of

\frac{5 + 1}{cos ( x )} :

Minimum

(2 πn, 6),

Maximum

(π + 2 πn, - 6)

Popular Examples

f(x)=(3x+1)/(4x+2)

f (x) = \frac{3 x + 1}{4 x + 2}

y=sin(x)sec^2(x)

y = sin (x) sec^{2} (x)

y=(3x^4-2x^3-4x)^4

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

y = x^{2} + 8 - 5

f(x)=11x^2+7x+13

f (x) = 11 x^{2} + 7 x + 13

Frequently Asked Questions (FAQ)

What is the p(x)=(5+1)/(cos(x)) ?
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