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Popular >

range of 4x-x^2

Solution

range

4 x - x^{2}

Solution

f (x) \leq 4

+1

Interval Notation

(- \infty, 4]

Solution steps

Vertex of

4 x - x^{2} :

Maximum

(2, 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}) = (2, 4)

f (x) \leq 4

Popular Examples

intercepts of f(x)=(x^2+x-6)/(x-2)intercepts

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

inverse of f(x)=7-3x^3 inverse

f (x) = 7 - 3 x^{3}

range of 1/(x^2)range

\frac{1}{x ^{2}}

intercepts of (x^2+7x+1)/(2x^2-5x-3)intercepts

\frac{x ^{2} + 7 x + 1}{2 x ^{2} - 5 x - 3}

extreme f(x)=x^4-8x^3+8 extreme points

f (x) = x^{4} - 8 x^{3} + 8

Frequently Asked Questions (FAQ)

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