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Popular >

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

Solution

range

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

Solution

f (x) \geq - 1

+1

Interval Notation

[- 1, \infty)

Solution steps

Vertex of

2 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 = 2,

Vertex

(x_{v}, y_{v}) = (0, - 1)

f (x) \geq - 1

Popular Examples

domain of f(x)=x+16 domain

f (x) = x + 16

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

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

range of f(x)=2x^2+20x+48 range

f (x) = 2 x^{2} + 20 x + 48

intercepts of (-2x-9)/(4x-19)intercepts

\frac{- 2 x - 9}{4 x - 19}

asymptotes of f(x)=(3-3x)/(x-5)asymptotes

f (x) = \frac{3 - 3 x}{x - 5}

Frequently Asked Questions (FAQ)

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