What is the range of the function f(x) defined by f(x)=left{begin{array}{ll}-1, & x

Question

What is the range of the function f(x) defined by f(x)=left{begin{array}{ll}-1, & x<-2  x^{2}-4, & -2 leq x<0  x-4, & 0 leq x leq 4  0, & x>4end{array}right.

Accepted Answer

Step:1 ：Find the range of the function for each interval:Step:2 ：Interval 1: (x < -2), (f(x) = -1), range is (-1)Step:3 ：Interval 2: (-2 leq x < 0), (f(x) = x^2 - 4), range is ([-4, 0])Step:4 ：Interval 3: (0 leq x leq 4), (f(x) = x - 4), range is ([-4, 0])Step:5 ：Interval 4: (x > 4), (f(x) = 0), range is (0)Step:6 ：Combine the ranges from each interval to find the overall range of the function: ([-4, 0])Step:7 ：(boxed{[-4, 0]})

Answer

Step: 1 ：Find the range of the function for each interval:Step: 2 ：Interval 1: (x < -2), (f(x) = -1), range is (-1)Step: 3 ：Interval 2: (-2 leq x < 0), (f(x) = x^2 - 4), range is ([-4, 0])Step: 4 ：Interval 3: (0 leq x leq 4), (f(x) = x - 4), range is ([-4, 0])Step: 5 ：Interval 4: (x > 4), (f(x) = 0), range is (0)Step: 6 ：Combine the ranges from each interval to find the overall range of the function: ([-4, 0])Step: 7 ：(boxed{[-4, 0]})

What is the range of the function $f(x)$ defined by $f(x)=\left\{\begin{array}{ll}-1, & x< -2 \\ x^{2}-4, & -2 \leq x< 0 \\ x-4, & 0 \leq x \leq 4 \\ 0, & x> 4\end{array}\right.$

Answer

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