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Popular >

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

Solution

range

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

Solution

f (x) \geq - 4

+1

Interval Notation

[- 4, \infty)

Solution steps

Vertex of

x^{2} + 2 x - 3 :

Minimum

(- 1, - 4)

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}) = (- 1, - 4)

f (x) \geq - 4

Popular Examples

inverse of f(x)=16x^2+1 inverse

f (x) = 16 x^{2} + 1

critical f(x)= x/(x^2-1)critical points

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

symmetry-2x^2-2x-2 symmetry

- 2 x^{2} - 2 x - 2

asymptotes of f(x)= 2/(x+3)asymptotes

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

inverse of f(x)=(x+20)/(x-5)inverse

f (x) = \frac{x + 20}{x - 5}

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2+2x-3 ?
The range of f(x)=x^2+2x-3 is f(x)>=-4