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Popular >

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

Solution

range

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

Solution

f (x) \geq 0

+1

Interval Notation

[0, \infty)

Solution steps

Vertex of

x^{2} + 2 x + 1 :

Minimum

(- 1, 0)

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, 0)

f (x) \geq 0

Popular Examples

range of r(x)= 1/(x-2)range

r (x) = \frac{1}{x - 2}

inflection x^{2/3}(1-x)inflection points

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

amplitude of-4-2cos(5x)amplitude

- 4 - 2 cos (5 x)

inverse of f(x)=x^{1/3}-9 inverse

f (x) = x^{\frac{1}{3}} - 9

parity f(x)=(4x^2-5)/(2x^3+x)parity

f (x) = \frac{4 x ^{2} - 5}{2 x ^{3} + x}

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2+2x+1 ?
The range of f(x)=x^2+2x+1 is f(x)>= 0