Given `f(x) = 1-|4-x^2|` show the y-intercept, natural domain and range. 

Expert Answers
justaguide eNotes educator| Certified Educator

The function f(x) = 1 - |4 - x^2|

At the y-intercept, x = 0, 1 - |4 - x^2| = 1 - 4 = -3. The y-intercept is (0, -3)

The domain of the function is the set of real numbers R. The range is the set `[1, -oo}`

aruv | Student


`|x|=x if x>=0`

`|x|=-x if x<0`


`f(x)=1-(4-x^2) if (4-x^2)>=0`




`f(x)=1-(-(4-x^2)) if (4-x^2)<0`



`f(x)=-3+x^2 if x in[-2,2]`

`` `f(x)=5-x^2 if x in (-oo,-2)U(2,oo)`

Because `0 in[-2,2]`  , so y intercept is


Thus y intercept is -3

because f(x) is defined for all real values of x so domain of f = set of real numbers= R

Range of f = `(-oo,1]`  because when `x=+-2 ,`  f(x)=1,

for remaing values it will be negative.

These all above discussion you can see in graph below.