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Popular Functions >

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

Solution

range

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

Solution

f (x) \leq \frac{9}{4}

+1

Interval Notation

(- \infty, \frac{9}{4}]

Solution steps

Vertex of

3 x - x^{2} :

Maximum

(\frac{3}{2}, \frac{9}{4})

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}) = (\frac{3}{2}, \frac{9}{4})

f (x) \leq \frac{9}{4}

Graph

Popular Examples

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extreme-0.1t^2+1.2t+98.8

inverse of f(x)=((x-7))/(2x+1)

Frequently Asked Questions (FAQ)

What is the range of f(x)=3x-x^2 ?
The range of f(x)=3x-x^2 is f(x)<= 9/4