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Popular >

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

Popular Examples

domain of f(x)=10x-9 domain

f (x) = 10 x - 9

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

f (x) = \frac{x + 2}{x ^{2} + 6 x + 8}

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

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

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

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

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

f (x) = \frac{x + 7}{x ^{3} - 3 x ^{2} + 5 x + 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