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Popular >

range of y=x^2-1

Solution

range

y = x^{2} - 1

Solution

f (x) \geq - 1

+1

Interval Notation

[- 1, \infty)

Solution steps

Vertex of

x^{2} - 1 :

Minimum

(0, - 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}) = (0, - 1)

f (x) \geq - 1

Popular Examples

inverse of y=-8x+3 inverse

y = - 8 x + 3

midpoint (-8,-2),(-7,8)midpoint

(- 8, - 2), (- 7, 8)

domain of f(x)= 1/(sqrt(6+x))domain

f (x) = \frac{1}{6 + x}

range of f(x)= 2/(sqrt(x-3))range

f (x) = \frac{2}{x - 3}

asymptotes of f(x)=(x-6)/(x^2+2)asymptotes

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

Frequently Asked Questions (FAQ)

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