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Popular Calculus >

f(x)=4cos(2x)

Solution

f (x) = 4 cos (2 x)

Solution

Period : π

Domain : - \infty < x < \infty

Range : - 4 \leq f (x) \leq 4

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

Asymptotes : None

Extreme Points : Maximum (πn, 4), Minimum (\frac{π}{2} + πn, - 4)

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Interval Notation

Domain : (- \infty, \infty)

Range : [- 4, 4]

Solution steps

Periodicity of

4 cos (2 x) : π

Domain of

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

Range of

4 cos (2 x) : - 4 \leq f (x) \leq 4

Axis interception points of

4 cos (2 x) :

X Intercepts

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

Y Intercepts

: (0, 4)

Asymptotes of

4 cos (2 x) :

None

Extreme Points of

4 cos (2 x) :

Maximum

(πn, 4),

Minimum

(\frac{π}{2} + πn, - 4)

Graph

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