evaluate f(-3), f(0), and f(2) given f(x) = {5 if x<2, 1/2 x-3 if x>=2

To evaluate \( f(-3) \), \( f(0) \), and \( f(2) \), we first examine the piecewise function:

\[
f(x) = 
\begin{cases} 
5 & \text{if } x < 2 \\
\frac{1}{2}x - 3 & \text{if } x \geq 2 
\end{cases}
\]

Now, let's evaluate each case:

1. **Evaluate \( f(-3) \):**
   Since \( -3 < 2 \), we use \( f(x) = 5 \):
   \[
   f(-3) = 5
   \]

2. **Evaluate \( f(0) \):**
   Since \( 0 < 2 \), we use \( f(x) = 5 \):
   \[
   f(0) = 5
   \]

3. **Evaluate \( f(2) \):**
   Since \( 2 \geq 2 \), we use \( f(x) = \frac{1}{2}x - 3 \):
   \[
   f(2) = \frac{1}{2}(2) - 3 = 1 - 3 = -2
   \]

### Final Results:
\[
f(-3) = 5, \quad f(0) = 5, \quad f(2) = -2
\]

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. What is \( f(4) \) given the same function?
2. For what values of \( x \) is \( f(x) = 0 \)?
3. How would the function change if the condition for \( x \geq 2 \) became \( x > 2 \)?
4. What happens to the function if we modify \( f(x) = \frac{1}{2}x - 3 \) to \( f(x) = x - 3 \) for \( x \geq 2 \)?
5. Can you sketch the graph of this piecewise function?

**Tip:** Always check the condition of a piecewise function before evaluating.

Evaluate f(-3), f(0), and f(2) given f(x) = {5 if x < 2, 1/2 x - 3 if x >= 2}.

Explore how to evaluate the piecewise function f(x) at x = -3, 0, and 2. Learn to apply conditions for x < 2 and x >= 2, using algebraic methods to find the correct function value at each point. This problem is suitable for students in Grades 9-11.

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