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Popular >

range of f(x)=x^2-4x-3

Solution

range

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

Solution

f (x) \geq - 7

+1

Interval Notation

[- 7, \infty)

Solution steps

Vertex of

x^{2} - 4 x - 3 :

Minimum

(2, - 7)

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}) = (2, - 7)

f (x) \geq - 7

Popular Examples

inverse of f(x)=1+x inverse

f (x) = 1 + x

asymptotes of y=((2x+2))/(3x+1)asymptotes

y = \frac{( 2 x + 2 )}{3 x + 1}

extreme f(x)=x^3+x^2-5x-2 extreme points

f (x) = x^{3} + x^{2} - 5 x - 2

inverse of f(x)= 3/(4x)-5 inverse

f (x) = \frac{3}{4 x} - 5

range of f(x)=2-x^2,-4<= x<= 4 range

f (x) = 2 - x^{2}, - 4 \leq x \leq 4

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2-4x-3 ?
The range of f(x)=x^2-4x-3 is f(x)>=-7