https://file.aiquickdraw.com/mathbot/file/1727099702287ub0e2qxe.jpg

Sketch the graph of:

please provide an image of the graph

Here is the graph of the piecewise function \( f(x) \) defined as:

\[
f(x) = 
\begin{cases} 
5 & \text{if } x < -3, \\
x + 1 & \text{if } -3 \leq x < 0, \\
-x^2 + 1 & \text{if } x \geq 0.
\end{cases}
\]

The graph consists of three different segments corresponding to each piece of the function:
1. A horizontal line at \( y = 5 \) for \( x < -3 \).
2. A linear segment with a slope of 1 from \( x = -3 \) to \( x = 0 \).
3. A downward-opening parabola starting from \( x = 0 \).

The red points mark the transitions at \( x = -3 \) and \( x = 0 \).

Would you like more details or have any questions about this graph? Here are some additional questions to expand your understanding:

1. What are the domain and range of this piecewise function?
2. How would you determine the continuity of this function at the transition points \( x = -3 \) and \( x = 0 \)?
3. What are the intercepts of the graph with the axes?
4. How does the behavior of the function change at each interval?
5. How would you describe the symmetry of the function, if any?

**Tip:** When sketching a piecewise function, it's crucial to clearly indicate the different intervals and ensure you identify and plot any transition points.

Sketch the graph of the piecewise function f(x) defined as:

f(x) = 
{ 5, if x < -3; x + 1, if -3 ≤ x < 0; -x² + 1, if x ≥ 0 }

Please provide an image of the graph.

Learn how to sketch the graph of a piecewise function with linear and quadratic components, including key points on transition behaviors and graph shapes for each interval. Suitable for Grades 9-11 students.

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