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Popular >

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

Solution

range

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

Solution

f (x) \leq 1

+1

Interval Notation

(- \infty, 1]

Solution steps

Vertex of

1 - (x - 2)^{2} :

Maximum

(2, 1)

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, 1)

f (x) \leq 1

Popular Examples

slope of 4x-2y=18 slope

4 x - 2 y = 18

domain of (x^2+x-12)/(x-3)domain

\frac{x ^{2} + x - 12}{x - 3}

slope ofintercept y+1=2x slope intercept

y + 1 = 2 x

inverse of f(x)=x+13 inverse

f (x) = x + 13

range of e^{x+2}-2 range

e^{x + 2} - 2

Frequently Asked Questions (FAQ)

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