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Popular Calculus >

f(x)=-2cos(2x)

Solution

f (x) = - 2 cos (2 x)

Solution

Period : π

Domain : - \infty < x < \infty

Range : - 2 \leq f (x) \leq 2

X Intercepts : (\frac{π}{4} + πn, 0), (\frac{3 π}{4} + πn, 0), Y Intercepts : (0, - 2)

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 2, 2]

Solution steps

Periodicity of

- 2 cos (2 x) : π

Domain of

- 2 cos (2 x) : - \infty < x < \infty

Range of

- 2 cos (2 x) : - 2 \leq f (x) \leq 2

Axis interception points of

- 2 cos (2 x) :

X Intercepts

: (\frac{π}{4} + πn, 0), (\frac{3 π}{4} + πn, 0),

Y Intercepts

: (0, - 2)

Asymptotes of

- 2 cos (2 x) :

None

Extreme Points of

- 2 cos (2 x) :

Minimum

(πn, - 2),

Maximum

(\frac{π}{2} + πn, 2)

Graph

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