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Popular >

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

Solution

range

f (x) = 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

intercepts of f(x)=-2x^3-8x^2+10x intercepts

f (x) = - 2 x^{3} - 8 x^{2} + 10 x

inverse of f(8)=(x^3)/4+6 inverse

f (8) = \frac{x ^{3}}{4} + 6

slope ofintercept 2-(8y+3x)/3 =6 slope intercept

2 - \frac{8 y + 3 x}{3} = 6

asymptotes of f(x)= 1/(1-x^2)asymptotes

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

inflection x^4-4x^3+3 inflection points

x^{4} - 4 x^{3} + 3

Frequently Asked Questions (FAQ)

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