Suppose that the function $$ f $$ is defined on the interval $$ [-2,2) $$ as follows. $$ f(x)=\left\{\begin{array}{ll}-2 & \text { if }-2 \leq x

Question

Suppose that the function $$ f $$ is defined on the interval $$ [-2,2) $$ as follows. $$ f(x)=\left\{\begin{array}{ll}-2 & \text { if }-2 \leq x<-1 \ -1 & \text { if }-1 \leq x<0 \ 0 & \text { if } 0 \leq x<1 \ 1 & \text { if } 1 \leq x<2\end{array}\right. $$ Find $$ f(-2), f(-0.5) $$, and $$ f(1) $$. $$ f(-2)=\square $$

UpStudy AI · Accepted Answer

The function $$ f $$ is defined piecewise on the interval $$[-2,2)$$:

1. For $$ -2 \leq x < -1 $$, $$ f(x) = -2 $$.
2. For $$ -1 \leq x < 0 $$, $$ f(x) = -1 $$.
3. For $$ 0 \leq x < 1 $$, $$ f(x) = 0 $$.
4. For $$ 1 \leq x < 2 $$, $$ f(x) = 1 $$.

To find the values:

- **Finding $$ f(-2) $$:**  
  Since $$-2$$ satisfies $$ -2 \leq -2 < -1 $$, we use the first piece.  
  Thus,  
  $$
  f(-2) = -2.
  $$

- **Finding $$ f(-0.5) $$:**  
  $$-0.5$$ satisfies $$ -1 \leq -0.5 < 0 $$, so we use the second piece.  
  Thus,  
  $$
  f(-0.5) = -1.
  $$

- **Finding $$ f(1) $$:**  
  $$1$$ satisfies $$1 \leq 1 < 2$$, so we use the fourth piece.  
  Thus,  
  $$
  f(1) = 1.
  $$

The final answers are:

$$
f(-2) = -2, \quad f(-0.5) = -1, \quad f(1) = 1.
$$
$$ f(-2) = -2 $$, $$ f(-0.5) = -1 $$, and $$ f(1) = 1 $$.

Suppose that the function is defined on the interval as follows.

Find , and .

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