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Popular >

y=4sin(x+45)+3

Solution

y = 4 sin (x + 4 5^{\circ}) + 3

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - 1 \leq f (x) \leq 7

X Intercepts : (- arcsin (\frac{3}{4}) + \frac{7 π}{4} + 2 πn, 0), (π + arcsin (\frac{3}{4}) - \frac{π}{4} + 2 πn, 0), Y Intercepts : (0, 22 + 3)

Asymptotes : None

Extreme Points : Maximum (\frac{π}{4} + 2 πn, 7), Minimum (\frac{5 π}{4} + 2 πn, - 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 7]

Solution steps

Convert

45

degrees to radians:

\frac{π}{4}

4 sin (x + \frac{π}{4}) + 3

Periodicity of

4 sin (x + \frac{π}{4}) + 3 : 2 π

Domain of

4 sin (x + \frac{π}{4}) + 3 : - \infty < x < \infty

Range of

4 sin (x + \frac{π}{4}) + 3 : - 1 \leq f (x) \leq 7

Axis interception points of

4 sin (x + \frac{π}{4}) + 3 :

X Intercepts

: (- arcsin (\frac{3}{4}) + \frac{7 π}{4} + 2 πn, 0), (π + arcsin (\frac{3}{4}) - \frac{π}{4} + 2 πn, 0),

Y Intercepts

: (0, 22 + 3)

Asymptotes of

4 sin (x + \frac{π}{4}) + 3 :

None

Extreme Points of

4 sin (x + \frac{π}{4}) + 3 :

Maximum

(\frac{π}{4} + 2 πn, 7),

Minimum

(\frac{5 π}{4} + 2 πn, - 1)

Popular Examples

f(x)=x^{10}+x^5-20

f (x) = x^{10} + x^{5} - 20

y=(arcsin(2x))/(arccos(2x))

y = \frac{arcsin ( 2 x )}{arccos ( 2 x )}

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

f (x) = \frac{x ^{2}}{( x ^{2} + 3 )}

f (x) = 4 - (x - 1)^{2}

f(x)=sec^4(x)tan^4(x)

f (x) = sec^{4} (x) tan^{4} (x)

Frequently Asked Questions (FAQ)

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