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Popular >

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

Solution

range

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

Solution

f (x) \leq 3

+1

Interval Notation

(- \infty, 3]

Solution steps

Vertex of

3 - x^{2} :

Maximum

(0, 3)

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, 3)

f (x) \leq 3

Popular Examples

intercepts of f(x)=(x^2-2x-15)/(x^2+3x)intercepts

f (x) = \frac{x ^{2} - 2 x - 15}{x ^{2} + 3 x}

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

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

domain of f(x)=sqrt(x+8)-(sqrt(5-x))/x domain

f (x) = x + 8 - \frac{5 - x}{x}

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

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

asymptotes of (x-1)/(x+3)asymptotes

\frac{x - 1}{x + 3}

Frequently Asked Questions (FAQ)

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