Evaluate the piecewise function when $$ x=-8 $$ and $$ x=-3 $$ $$ f(x)=\left\{\begin{array}{l}3 x-7 ext {, if } x

Question

Evaluate the piecewise function when $$ x=-8 $$ and $$ x=-3 $$ $$ f(x)=\left\{\begin{array}{l}3 x-7 	ext {, if } x<-3 \ -2 x, 	ext { if } x \geq-3\end{array}ight. $$ The value of $$ f $$ is $$ \square $$ when $$ x=-8 $$. The value of $$ f $$ is $$ \square $$ when $$ x=-3 $$.

UpStudy AI · Accepted Answer

To evaluate the piecewise function $$ f(x) $$ at $$ x = -8 $$ and $$ x = -3 $$, we'll use the given definition:

$$
f(x) = \begin{cases}
3x - 7 & \text{if } x < -3 \
-2x & \text{if } x \geq -3
\end{cases}
$$

### 1. Evaluating $$ f(-8) $$:

- **Determine which piece to use:** Since $$ -8 < -3 $$, we use the first piece of the function.
  
$$
f(-8) = 3(-8) - 7 = -24 - 7 = -31
$$

### 2. Evaluating $$ f(-3) $$:

- **Determine which piece to use:** Since $$ -3 \geq -3 $$, we use the second piece of the function.
  
$$
f(-3) = -2(-3) = 6
$$

### **Final Answers:**

- The value of $$ f $$ when $$ x = -8 $$ is $$ \boxed{-31} $$.
- The value of $$ f $$ when $$ x = -3 $$ is $$ \boxed{6} $$.
When $$ x = -8 $$, $$ f(x) = -31 $$. When $$ x = -3 $$, $$ f(x) = 6 $$.

Evaluate the piecewise function when \( x=-8 \) and \( x=-3 \) \( f(x)=\left\{\begin{array}{l}3 x-7 \text {, if } x<-3 \\ -2 x, \text { if } x \geq-3\end{array}\right. \) The value of \( f \) is \( \square \) when \( x=-8 \). The value of \( f \) is \( \square \) when \( x=-3 \).

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