en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

range of f(x)=4-(x-3)^2

Solution

range

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

Solution

f (x) \leq 4

+1

Interval Notation

(- \infty, 4]

Solution steps

Vertex of

4 - (x - 3)^{2} :

Maximum

(3, 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}) = (3, 4)

f (x) \leq 4

Popular Examples

intercepts of (x^2-16)/(2x^2-11x+12)intercepts

\frac{x ^{2} - 16}{2 x ^{2} - 11 x + 12}

midpoint (-1,4),(5,-6)midpoint

(- 1, 4), (5, - 6)

parity f(x)=-5x^3 parity

f (x) = - 5 x^{3}

line m= 13/20 ,(20,9)line

m = \frac{13}{20}, (20, 9)

inverse of f(x)=2\sqrt[3]{x-3}inverse

Frequently Asked Questions (FAQ)

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