What is the f(x)=-1/2 cos(8x)-1/2 sin(8x) ?

The f(x)=-1/2 cos(8x)-1/2 sin(8x) is

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f(x)=-1/2 cos(8x)-1/2 sin(8x)

f (x) = - \frac{1}{2} cos (8 x) - \frac{1}{2} sin (8 x)

Period : π

Domain : - \infty < x < \infty

Range : - \frac{2}{2} \leq f (x) \leq \frac{2}{2}

X Intercepts : (\frac{3 π}{32} + πn, 0), (\frac{7 π}{32} + πn, 0), (\frac{11 π}{32} + πn, 0), (\frac{15 π}{32} + πn, 0), (\frac{19 π}{32} + πn, 0), (\frac{23 π}{32} + πn, 0), (\frac{27 π}{32} + πn, 0), (\frac{31 π}{32} + πn, 0), Y Intercepts : (0, - \frac{1}{2})

Asymptotes : None

Extreme Points : Minimum (\frac{π}{32} + πn, - \frac{1}{2}), Maximum (\frac{5 π}{32} + πn, \frac{1}{2}), Minimum (\frac{9 π}{32} + πn, - \frac{1}{2}), Maximum (\frac{13 π}{32} + πn, \frac{1}{2}), Minimum (\frac{17 π}{32} + πn, - \frac{1}{2}), Maximum (\frac{21 π}{32} + πn, \frac{1}{2}), Minimum (\frac{25 π}{32} + πn, - \frac{1}{2}), Maximum (\frac{29 π}{32} + πn, \frac{1}{2})

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{2}{2}, \frac{2}{2}]

Solution steps

Periodicity of

- \frac{1}{2} cos (8 x) - \frac{1}{2} sin (8 x) : π

Domain of

- \frac{1}{2} cos (8 x) - \frac{1}{2} sin (8 x) : - \infty < x < \infty

Range of

- \frac{1}{2} cos (8 x) - \frac{1}{2} sin (8 x) : - \frac{2}{2} \leq f (x) \leq \frac{2}{2}

Axis interception points of

- \frac{1}{2} cos (8 x) - \frac{1}{2} sin (8 x) :

X Intercepts

: (\frac{3 π}{32} + πn, 0), (\frac{7 π}{32} + πn, 0), (\frac{11 π}{32} + πn, 0), (\frac{15 π}{32} + πn, 0), (\frac{19 π}{32} + πn, 0), (\frac{23 π}{32} + πn, 0), (\frac{27 π}{32} + πn, 0), (\frac{31 π}{32} + πn, 0),

Y Intercepts

: (0, - \frac{1}{2})

Asymptotes of

- \frac{1}{2} cos (8 x) - \frac{1}{2} sin (8 x) :

None

Extreme Points of

- \frac{1}{2} cos (8 x) - \frac{1}{2} sin (8 x) :

Minimum

(\frac{π}{32} + πn, - \frac{1}{2}),

Maximum

(\frac{5 π}{32} + πn, \frac{1}{2}),

Minimum

(\frac{9 π}{32} + πn, - \frac{1}{2}),

Maximum

(\frac{13 π}{32} + πn, \frac{1}{2}),

Minimum

(\frac{17 π}{32} + πn, - \frac{1}{2}),

Maximum

(\frac{21 π}{32} + πn, \frac{1}{2}),

Minimum

(\frac{25 π}{32} + πn, - \frac{1}{2}),

Maximum

(\frac{29 π}{32} + πn, \frac{1}{2})

f (x) = \frac{x ^{2} - 7 x + 12}{x - 3}

f (x) = \frac{4 x ^{2} - 16}{x - 2}

f (x) = 2 + 3 (4^{x})

f (x) = \frac{12 + x - x ^{2}}{∣ 2 x - 5 ∣}

f (x) = \frac{cos ( x )}{cot ( x )}

What is the f(x)=-1/2 cos(8x)-1/2 sin(8x) ?
The f(x)=-1/2 cos(8x)-1/2 sin(8x) is