The given function $f(x)$ is written in a piecewise form, although it is currently not completely clear. To properly evaluate $f(x)$ at the specified points, we need to understand the piecewise intervals and conditions for $f(x)$. I will assume the function should be expressed like this:

\begin{cases} 3x - 14 & \text{if } -10 < x < 1, \\ x + 2 & \text{if } 2 < x < 10 \end{cases}$$ Now, let's evaluate $$f(x)$$ at each given $$x$$-value: 1. **At $$x = -3$$:** $$-10 < -3 < 1, \text{ so } f(x) = 3x - 14.$$ $$f(-3) = 3(-3) - 14 = -9 - 14 = -23.$$ 2. **At $$x = -8$$:** $$-10 < -8 < 1, \text{ so } f(x) = 3x - 14.$$ $$f(-8) = 3(-8) - 14 = -24 - 14 = -38.$$ 3. **At $$x = -10$$:** $$x = -10$$ is **not included** in the interval $$-10 < x < 1$$, so $$f(-10)$$ is undefined. 4. **At $$x = -12$$:** $$x = -12$$ is **outside** both intervals $$-10 < x < 1$$ and $$2 < x < 10$$, so $$f(-12)$$ is undefined. 5. **At $$x = -14$$:** Similar to $$x = -12$$, $$x = -14$$ is also outside both intervals, so $$f(-14)$$ is undefined. ### Summary: - $$f(-3) = -23$$ - $$f(-8) = -38$$ - $$f(-10), f(-12), f(-14)$$ are **undefined**. Would you like more details, or do you have any questions? Here are some related questions to explore: 1. What is the value of $$f(x)$$ at $$x = 0$$? 2. How do we interpret discontinuities in piecewise functions? 3. How would we rewrite $$f(x)$$ if the intervals changed? 4. Can piecewise functions have overlapping intervals? 5. How do we handle boundary points in piecewise functions? **Tip:** Always pay attention to whether intervals are open ( $$<$$, $$>$$ ) or closed ( $$\leq$$, $$\geq$$ ) to avoid including undefined points.