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

Question

Suppose that the function $$ f $$ is defined on the interval $$ [-2,2) $$ as follows. $$ f(x)=\left\{\begin{array}{ll}-2 & 	ext { if }-2 \leq x<-1 \ -1 & 	ext { if }-1 \leq x<0 \ 0 & 	ext { if } 0 \leq x<1 \ 1 & 	ext { if } 1 \leq x<2\end{array}ight. $$ Find $$ f(-2), f(-0.75) $$, and $$ f(1) $$ $$ f(-2)=\square $$ $$ f(-0.75)=\square $$

UpStudy AI · Accepted Answer

To find the values of the function $$ f $$ at the specified points, we will evaluate each one based on the piecewise definition of $$ f $$.

1. **Finding $$ f(-2) $$**:
   - We check which interval $$ -2 $$ falls into:
     - The first interval is $$ -2 \leq x < -1 $$.
   - Since $$ -2 $$ is included in this interval, we have:
     $$
     f(-2) = -2
     $$

2. **Finding $$ f(-0.75) $$**:
   - We check which interval $$ -0.75 $$ falls into:
     - The second interval is $$ -1 \leq x < 0 $$.
   - Since $$ -0.75 $$ is in this interval, we have:
     $$
     f(-0.75) = -1
     $$

3. **Finding $$ f(1) $$**:
   - We check which interval $$ 1 $$ falls into:
     - The fourth interval is $$ 1 \leq x < 2 $$.
   - Since $$ 1 $$ is included in this interval, we have:
     $$
     f(1) = 1
     $$

Thus, the values are:
$$
f(-2) = -2
$$
$$
f(-0.75) = -1
$$
$$
f(1) = 1
$$

In summary:
- $$ f(-2) = -2 $$
- $$ f(-0.75) = -1 $$
- $$ f(1) = 1 $$
$$ f(-2) = -2 $$ $$ f(-0.75) = -1 $$ $$ f(1) = 1 $$

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