What is the range of f(x)=sqrt(1-|x|) ?

The range of f(x)=sqrt(1-|x|) is 0<= f(x)<= 1

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range of f(x)=sqrt(1-|x|)

range

f (x) = 1 - ∣ x ∣

0 \leq f (x) \leq 1

Interval Notation

[0, 1]

Solution steps

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

Domain of

1 - ∣ x ∣ : - 1 \leq x \leq 1

Extreme Points of

1 - ∣ x ∣ :

Minimum

(- 1, 0),

Maximum

(0, 1),

Minimum

(1, 0)

Absolute value functions are piecewise functions

Find the function intervals:

- 1 \leq x < 0, 0 \leq x \leq 1

Evaluate the function behavior for each interval

Find the range for the interval

- 1 \leq x < 0 : 0 \leq f (x) < 1

Find the range for the interval

0 \leq x \leq 1 : 0 \leq f (x) \leq 1

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

0 \leq f (x) < 1 or 0 \leq f (x) \leq 1

0 \leq f (x) \leq 1

lo g_{2} (lo g_{2} (n))

\frac{x ^{2} + 2 x - 15}{2 x ^{2} + 16 x + 30}

f (x) = \frac{9}{( x - 2 ) ^{2}}

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

- 2 + sin (x + \frac{π}{3})

What is the range of f(x)=sqrt(1-|x|) ?
The range of f(x)=sqrt(1-|x|) is 0<= f(x)<= 1