https://file.aiquickdraw.com/mathbot/file/1726783737695l6f0x8gs.jpg

The piecewise function provided in the image is:

\[
f(x) = 
\begin{cases} 
2x & \text{if } x < 0 \\
-8x + 3 & \text{if } x \geq 0
\end{cases}
\]

To graph this function:

1. **For \( x < 0 \):** The function is \( f(x) = 2x \). This is a straight line with a slope of 2, passing through the origin (0,0). However, since this function is only valid for \( x < 0 \), we draw this line only for negative \( x \)-values.

2. **For \( x \geq 0 \):** The function is \( f(x) = -8x + 3 \). This is a straight line with a slope of -8 and a y-intercept of 3. This part is only valid for \( x \geq 0 \).

Here is a breakdown of how the graph would look:

- For \( x < 0 \), plot points for negative \( x \)-values (like \( x = -1, -2 \)) and find the corresponding \( y \)-values using the equation \( 2x \).
- For \( x \geq 0 \), plot points for non-negative \( x \)-values (like \( x = 0, 1 \)) using the equation \( -8x + 3 \).
- At \( x = 0 \), the value from \( -8x + 3 \) is \( 3 \), so there is a point at \( (0, 3) \).

Would you like me to plot the graph for you, or do you want details on any specific aspect?

Here are 5 related questions:
1. What happens if we modify the slopes in this piecewise function?
2. How do you find the slope of each part of a piecewise function graphically?
3. What is the domain and range of the given piecewise function?
4. How does the graph change if the conditions on \( x \) are swapped?
5. How can you identify discontinuities in a piecewise function graph?

**Tip:** When graphing piecewise functions, always check if the transition points are continuous or if there’s a jump (discontinuity).

Graph the piecewise function: f(x) = { 2x if x < 0, -8x + 3 if x ≥ 0 }

Learn how to graph the piecewise function f(x) = { 2x if x < 0, -8x + 3 if x ≥ 0 } with step-by-step instructions. Explore the graphical representation of linear functions in different intervals. Suitable for high school students studying algebra and graphing.

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