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Popular >

f(x)=4cos(x/2+pi/4)+4

Solution

f (x) = 4 cos (\frac{x}{2} + \frac{π}{4}) + 4

Solution

Period : 4 π

Domain : - \infty < x < \infty

Range : 0 \leq f (x) \leq 8

X Intercepts : (2 π - \frac{π}{2} + 4 πn, 0), Y Intercepts : (0, 22 + 4)

Asymptotes : None

Extreme Points : Minimum (\frac{3 π}{2} + 4 πn, 0), Maximum (\frac{7 π}{2} + 4 πn, 8)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [0, 8]

Solution steps

Periodicity of

4 cos (\frac{x}{2} + \frac{π}{4}) + 4 : 4 π

Domain of

4 cos (\frac{x}{2} + \frac{π}{4}) + 4 : - \infty < x < \infty

Range of

4 cos (\frac{x}{2} + \frac{π}{4}) + 4 : 0 \leq f (x) \leq 8

Axis interception points of

4 cos (\frac{x}{2} + \frac{π}{4}) + 4 :

X Intercepts

: (2 π - \frac{π}{2} + 4 πn, 0),

Y Intercepts

: (0, 22 + 4)

Asymptotes of

4 cos (\frac{x}{2} + \frac{π}{4}) + 4 :

None

Extreme Points of

4 cos (\frac{x}{2} + \frac{π}{4}) + 4 :

Minimum

(\frac{3 π}{2} + 4 πn, 0),

Maximum

(\frac{7 π}{2} + 4 πn, 8)

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Frequently Asked Questions (FAQ)

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