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Popular >

range of f(x)=(x-3)^2+1

Solution

range

f (x) = (x - 3)^{2} + 1

Solution

f (x) \geq 1

+1

Interval Notation

[1, \infty)

Solution steps

Vertex of

(x - 3)^{2} + 1 :

Minimum

(3, 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}) = (3, 1)

f (x) \geq 1

Popular Examples

critical f(x)=(x+8)/(x+1)critical points

f (x) = \frac{x + 8}{x + 1}

parity x/(x^2-6x+8)parity

\frac{x}{x ^{2} - 6 x + 8}

inverse of ln(x-3)inverse

ln (x - 3)

domain of (7-10x)/(3x+10)domain

\frac{7 - 10 x}{3 x + 10}

extreme f(x)=x^3-75x extreme points

f (x) = x^{3} - 75 x

Frequently Asked Questions (FAQ)

What is the range of f(x)=(x-3)^2+1 ?
The range of f(x)=(x-3)^2+1 is f(x)>= 1