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

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

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

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

Period : π

Domain : - \infty < x < \infty

Range : 0 \leq f (x) \leq 1

X Intercepts : (πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Minimum (πn, 0), Maximum (\frac{π}{2} + πn, 1)

Interval Notation

Domain : (- \infty, \infty)

Range : [0, 1]

Solution steps

Periodicity of

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

Domain of

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

Range of

\frac{sin ^{2} ( x )}{1 + cos ^{2} ( x )} : 0 \leq f (x) \leq 1

Axis interception points of

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

X Intercepts

: (πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

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

None

Extreme Points of

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

Minimum

(πn, 0),

Maximum

(\frac{π}{2} + πn, 1)

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

f (x) = x^{2} - 12 x - 36

f (x) = x^{2} - 12 x + 34

f (x) = lo g_{10} (x) + 2