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Popular >

range of f(x)=-x^2-6x+1

Solution

range

f (x) = - x^{2} - 6 x + 1

Solution

f (x) \leq 10

+1

Interval Notation

(- \infty, 10]

Solution steps

Vertex of

- x^{2} - 6 x + 1 :

Maximum

(- 3, 10)

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}) = (- 3, 10)

f (x) \leq 10

Popular Examples

parity y= x/(x^3-x+5)parity

y = \frac{x}{x ^{3} - x + 5}

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

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

inverse of (1-e^{-x})/(1+e^{-x)}inverse

\frac{1 - e ^{- x}}{1 + e ^{- x}}

line (0.54,10^{16}),(1307.9,10^{17})line

(0.54, 1 0^{16}), (1307.9, 1 0^{17})

domain of sqrt(1/x+2)domain

\frac{1}{x} + 2

Frequently Asked Questions (FAQ)

What is the range of f(x)=-x^2-6x+1 ?
The range of f(x)=-x^2-6x+1 is f(x)<= 10