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Given `f(x) = 1-|4-x^2|` show the y-intercept, natural domain and range.
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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}`
Posted by justaguide on June 12, 2013 at 4:49 PM (Answer #1)
High School Teacher
`|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.
Posted by aruv on June 13, 2013 at 7:54 AM (Answer #2)
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