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Popular Calculus >

f(x)=-4sin(4x)

Solution

f (x) = - 4 sin (4 x)

Solution

Period : \frac{π}{2}

Domain : - \infty < x < \infty

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

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

Asymptotes : None

Extreme Points : Minimum (\frac{π}{8} + \frac{π}{2} n, - 4), Maximum (\frac{3 π}{8} + \frac{π}{2} n, 4)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 4, 4]

Solution steps

Periodicity of

- 4 sin (4 x) : \frac{π}{2}

Domain of

- 4 sin (4 x) : - \infty < x < \infty

Range of

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

Axis interception points of

- 4 sin (4 x) :

X Intercepts

: (\frac{πn}{2}, 0), (\frac{π}{4} + \frac{πn}{2}, 0),

Y Intercepts

: (0, 0)

Asymptotes of

- 4 sin (4 x) :

None

Extreme Points of

- 4 sin (4 x) :

Minimum

(\frac{π}{8} + \frac{π}{2} n, - 4),

Maximum

(\frac{3 π}{8} + \frac{π}{2} n, 4)

Graph

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