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Popular >

range of f(x)=9-(x-2)^2

Solution

range

f (x) = 9 - (x - 2)^{2}

Solution

f (x) \leq 9

+1

Interval Notation

(- \infty, 9]

Solution steps

Vertex of

9 - (x - 2)^{2} :

Maximum

(2, 9)

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, 9)

f (x) \leq 9

Popular Examples

inverse of f(x)=6x^3-3 inverse

f (x) = 6 x^{3} - 3

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

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

frequency p(t)=161sin(6t+pi)frequency

p (t) = 161 sin (6 t + π)

critical f(x)=-125/4 x^4+x critical points

f (x) = - \frac{125}{4} x^{4} + x

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

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

Frequently Asked Questions (FAQ)

What is the range of f(x)=9-(x-2)^2 ?
The range of f(x)=9-(x-2)^2 is f(x)<= 9