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Popular Functions >

range of f(x)=(x-4)^2+1

Solution

range

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

Solution

f (x) \geq 1

+1

Interval Notation

[1, \infty)

Solution steps

Vertex of

(x - 4)^{2} + 1 :

Minimum

(4, 1)

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}) = (4, 1)

f (x) \geq 1

Graph

Popular Examples

domain of f(x)=10x-9

domain of f(x)=(x+2)/(x^2+6x+8)

perpendicular y=-8x+7,(5,-3)

critical f(x)=x^4-12x^3+16x^2

parity f(x)=(x+7)/(x^3-3x^2+5x+2)

Frequently Asked Questions (FAQ)

What is the range of f(x)=(x-4)^2+1 ?
The range of f(x)=(x-4)^2+1 is f(x)>= 1