Determine the values of f(x) when x is less than -3:
$f(x)=\left\{\begin{array}{ll}-3 x+5 & \text { if } x< -3 \\ 5 & \text { if }-3 \leq x \leq 3 \\ -x+14 & \text { if } x> 3\end{array}\right.$
Answer
\(\boxed{\text{Final Answer: The values of } f(x) \text{ when } x \text{ is less than } -3 \text{ are given by the function } -3x + 5. \text{ The values of } f(x) \text{ range from } 5 \text{ to } 35 \text{ when } x \text{ is in the interval } [-10, -3].}\)
Step 1 ：We are given the piecewise function $f(x)=\left\{\begin{array}{ll}-3 x+5 & \text { if } x<-3 \\ 5 & \text { if }-3 \leq x \leq 3 \\ -x+14 & \text { if } x>3\end{array}\right.$
Step 2 ：We are asked to determine the values of $f(x)$ when $x$ is less than $-3$. From the given function, we can see that when $x$ is less than $-3$, the function is defined as $-3x + 5$.
Step 3 ：Let's calculate the value of $-3x + 5$ for $x < -3$.
Step 4 ：We can plot the function $f(x)$ for $x$ in the interval $[-10, -3]$ to visualize the values of $f(x)$.
Step 5 ：From the plot, we can see that as $x$ decreases, $f(x)$ increases linearly. The values of $f(x)$ range from $5$ to $35$ when $x$ is in the interval $[-10, -3]$.
Step 6 ：\(\boxed{\text{Final Answer: The values of } f(x) \text{ when } x \text{ is less than } -3 \text{ are given by the function } -3x + 5. \text{ The values of } f(x) \text{ range from } 5 \text{ to } 35 \text{ when } x \text{ is in the interval } [-10, -3].}\)
