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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

range of 2(1/3)^x range

2 (\frac{1}{3})^{x}

perpendicular 3x+2y=-7,(1,1)perpendicular

3 x + 2 y = - 7, (1, 1)

domain of-3/x domain

- \frac{3}{x}

periodicity of y=-1/3 sin((5x)/4)periodicity

y = - \frac{1}{3} sin (\frac{5 x}{4})

asymptotes of f(x)= 1/x+1 asymptotes

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

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