Worksheet displaying piecewise functions and their corresponding graphs.

It looks like you've uploaded an image containing a math worksheet titled "10.2B: Piecewise Functions", which includes several problems related to piecewise functions. Since I can't view images directly, I’ll need you to provide the content of the image (e.g., text or description of the problems) so I can help solve and explain them.

However, based on the title and typical structure of such worksheets, here’s what you might expect:

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🔍 What is a Piecewise Function?

A piecewise function is defined by different expressions over different intervals of the domain. For example:
$$
f(x) =
\begin{cases}
x + 1 & \text{if } x < 0 \\
x^2 & \text{if } x \geq 0
\end{cases}
$$

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📌 Common Tasks in These Problems:

1. Evaluate the function at specific values.
2. Graph the piecewise function.
3. Write a rule for a given graph.
4. Determine domain and range.
5. Identify continuity or discontinuity.

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✔ Example Problem (Typical):

Suppose the problem says:

> Evaluate $ f(-2), f(0), f(3) $ for:
> $$
> f(x) =
> \begin{cases}
> 2x + 1 & \text{if } x < 1 \\
> x^2 - 1 & \text{if } x \geq 1
> \end{cases}
> $$

#### Solution:
- $ f(-2) $: since $-2 < 1$, use $2x + 1$:
$ 2(-2) + 1 = -4 + 1 = -3 $
- $ f(0) $: $0 < 1$, so $2(0) + 1 = 1$
- $ f(3) $: $3 \geq 1$, so $3^2 - 1 = 9 - 1 = 8$

✔ Answers: $ f(-2) = -3, f(0) = 1, f(3) = 8 $

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📈 Graphing a Piecewise Function:

You might be asked to graph something like:
$$
f(x) =
\begin{cases}
-2x + 4 & \text{if } x \leq 1 \\
x - 1 & \text{if } x > 1
\end{cases}
$$

Steps:
1. Graph $ y = -2x + 4 $ only for $ x \leq 1 $ (closed dot at $ x = 1 $).
2. Graph $ y = x - 1 $ only for $ x > 1 $ (open dot at $ x = 1 $).

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Please describe the specific problems from your image — for example:
- The function definitions
- The questions (evaluate, graph, etc.)
- Any graphs shown
- Multiple-choice options if present

Once I have that, I can give you step-by-step solutions and explanations tailored to your worksheet!