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Popular >

range of 4-x^2

Solution

range

4 - x^{2}

Solution

f (x) \leq 4

+1

Interval Notation

(- \infty, 4]

Solution steps

Vertex of

4 - x^{2} :

Maximum

(0, 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}) = (0, 4)

f (x) \leq 4

Popular Examples

extreme f(x)=(x+2)(-x)^{1/2}extreme points

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

symmetry y= x/(x^2+1)symmetry

y = \frac{x}{x ^{2} + 1}

line (38.7,38.24),(84.6,87.04)line

(38.7, 38.24), (84.6, 87.04)

midpoint (-1,6),(-6,-1)midpoint

(- 1, 6), (- 6, - 1)

inverse of f(x)=0.2x^2 inverse

f (x) = 0.2 x^{2}

Frequently Asked Questions (FAQ)

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