What is the f(x)=(1+sin^2(x))/(cos^2(x)) ?

The f(x)=(1+sin^2(x))/(cos^2(x)) is

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f(x)=(1+sin^2(x))/(cos^2(x))

f (x) = \frac{1 + sin ^{2} ( x )}{cos ^{2} ( x )}

Period : π

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

Range : f (x) \geq 1

Y Intercepts : (0, 1)

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

Extreme Points : Minimum (πn, 1)

Interval Notation

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

Range : [1, \infty)

Solution steps

Periodicity of

\frac{1 + sin ^{2} ( x )}{cos ^{2} ( x )} : π

Domain of

\frac{1 + sin ^{2} ( x )}{cos ^{2} ( x )} : πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Range of

\frac{1 + sin ^{2} ( x )}{cos ^{2} ( x )} : f (x) \geq 1

Axis interception points of

\frac{1 + sin ^{2} ( x )}{cos ^{2} ( x )} :

Y Intercepts

: (0, 1)

Asymptotes of

\frac{1 + sin ^{2} ( x )}{cos ^{2} ( x )} :

Vertical

: x = \frac{π}{2} + πn

Extreme Points of

\frac{1 + sin ^{2} ( x )}{cos ^{2} ( x )} :

Minimum

(πn, 1)

f (x) = ln (1 - 3 x)

f (x) = 2 + x - x^{2}

y = 2 x^{2} + 10

g (x) = 3 x^{2} - 1

f (x) = - 3 sin (\frac{1}{2}) x