What is the range of-sqrt(-x^2-4x+5)+3 ?

The range of-sqrt(-x^2-4x+5)+3 is 0<= f(x)<= 3

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range of-sqrt(-x^2-4x+5)+3

range

- - x^{2} - 4 x + 5 + 3

0 \leq f (x) \leq 3

Interval Notation

[0, 3]

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

- - x^{2} - 4 x + 5 + 3 : - 5 \leq x \leq 1

Extreme Points of

- - x^{2} - 4 x + 5 + 3 :

Maximum

(- 5, 3),

Minimum

(- 2, 0),

Maximum

(1, 3)

Find the range for the interval

- 5 \leq x \leq 1 : 0 \leq f (x) \leq 3

Combine the ranges of all domain intervals to obtain the function range

0 \leq f (x) \leq 3

f (x) = \frac{2}{3} x - 1

e^{x^{2} - 6 x + 8}

(- 8, - 10), (0, - 3)

m = - \frac{5}{2}, (1, 3)

X^{3}

What is the range of-sqrt(-x^2-4x+5)+3 ?
The range of-sqrt(-x^2-4x+5)+3 is 0<= f(x)<= 3