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Popular >

y=4sin(x-pi/2)-1

Solution

y = 4 sin (x - \frac{π}{2}) - 1

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - 5 \leq f (x) \leq 3

X Intercepts : (arcsin (\frac{1}{4}) + \frac{π}{2} + 2 πn, 0), (π - arcsin (\frac{1}{4}) + \frac{π}{2} + 2 πn, 0), Y Intercepts : (0, - 5)

Asymptotes : None

Extreme Points : Minimum (2 πn, - 5), Maximum (π + 2 πn, 3)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 5, 3]

Solution steps

Periodicity of

4 sin (x - \frac{π}{2}) - 1 : 2 π

Domain of

4 sin (x - \frac{π}{2}) - 1 : - \infty < x < \infty

Range of

4 sin (x - \frac{π}{2}) - 1 : - 5 \leq f (x) \leq 3

Axis interception points of

4 sin (x - \frac{π}{2}) - 1 :

X Intercepts

: (arcsin (\frac{1}{4}) + \frac{π}{2} + 2 πn, 0), (π - arcsin (\frac{1}{4}) + \frac{π}{2} + 2 πn, 0),

Y Intercepts

: (0, - 5)

Asymptotes of

4 sin (x - \frac{π}{2}) - 1 :

None

Extreme Points of

4 sin (x - \frac{π}{2}) - 1 :

Minimum

(2 πn, - 5),

Maximum

(π + 2 πn, 3)

Popular Examples

f(x)=2x^3+6x^2-5

f (x) = 2 x^{3} + 6 x^{2} - 5

f (x) = \frac{1}{3 x + 6}

f(x)=2x^3+6x^2+2

f (x) = 2 x^{3} + 6 x^{2} + 2

f (m) = m^{2} - 8 m + 15

y = - 5 x - 21

Frequently Asked Questions (FAQ)

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