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Popular Functions >

range of f(x)=(x-3)^2+5

Solution

range

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

Solution

f (x) \geq 5

+1

Interval Notation

[5, \infty)

Solution steps

Vertex of

(x - 3)^{2} + 5 :

Minimum

(3, 5)

For a parabola

a x^{2} + b x + c

with Vertex

(x_{v}, y_{v})

If

a < 0

the range is

f (x) \leq y_{v}

If

a > 0

the range is

f (x) \geq y_{v}

a = 1,

Vertex

(x_{v}, y_{v}) = (3, 5)

f (x) \geq 5

Graph

Popular Examples

critical f(x)=3x^4+4x^3

cr i t i c a l f (x) = 3 x^{4} + 4 x^{3}

range of f(x)=log_{1/20}(-x)

r an g e f (x) = lo g_{\frac{1}{20}} (- x)

asymptotes of f(x)= 6/(x-5)

a sy m pt o t es f (x) = \frac{6}{x - 5}

inverse of f(x)=2y^2

in v erse f (x) = 2 y^{2}

perpendicular 3x-y=8

p er p e n d i c u l a r 3 x - y = 8

Frequently Asked Questions (FAQ)

What is the range of f(x)=(x-3)^2+5 ?
The range of f(x)=(x-3)^2+5 is f(x)>= 5