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Let's go through the given problem step by step. The piecewise function \( f(x) \) is defined as follows:

\[
f(x) = 
\begin{cases}
-5, & \text{if } 2 \leq x < 3 \\
-4, & \text{if } 3 \leq x < 4 \\
-3, & \text{if } 4 \leq x < 5 \\
-2, & \text{if } 5 \leq x < 6 \\
-1, & \text{if } 6 \leq x < 7
\end{cases}
\]

We need to solve the following parts:

### (a) Domain of \( f \):
The domain of \( f \) is the set of all possible values of \( x \) for which \( f(x) \) is defined. From the piecewise definition, we see that the function is defined for \( 2 \leq x < 7 \).

So, the domain is:
\[
\boxed{[2, 7)}
\]

### (b) Range of \( f \):
The range of \( f \) is the set of all output values. The function takes the values \( -5, -4, -3, -2, -1 \) depending on the interval of \( x \).

Thus, the range is:
\[
\boxed{\{-5, -4, -3, -2, -1\}}
\]

### (c) \( f(2) \):
According to the first case of the piecewise function, when \( 2 \leq x < 3 \), \( f(x) = -5 \).

Thus, \( f(2) = \boxed{-5} \).

### (d) \( f(3) \):
For \( 3 \leq x < 4 \), the function value is \( f(x) = -4 \).

Thus, \( f(3) = \boxed{-4} \).

### (e) \( f(7) \):
The function is defined for \( x < 7 \) but not at \( x = 7 \) (since the interval is open at 7).

Thus, \( f(7) \) is **undefined**, so the answer is:
\[
\boxed{\text{undefined}}
\]

### (f) \( f(3.18) \):
For \( 3 \leq x < 4 \), we have \( f(x) = -4 \), and since \( 3.18 \) is in this interval, \( f(3.18) = -4 \).

Thus, \( f(3.18) = \boxed{-4} \).

### (g) \( f(\sqrt{20.14}) \):
First, we calculate \( \sqrt{20.14} \approx 4.49 \). This value falls in the interval \( 4 \leq x < 5 \), where \( f(x) = -3 \).

Thus, \( f(\sqrt{20.14}) = \boxed{-3} \).

---

Do you have any further questions, or would you like details on any step? Here are 5 related questions:

1. How can we determine whether a function is continuous at certain points?
2. What is the difference between a closed and open interval in domain definition?
3. Can a piecewise function have more than two cases? How would we represent that?
4. How do we find the range of more complex piecewise functions?
5. How can we graph a piecewise function like this?

**Tip:** When analyzing piecewise functions, always pay attention to the endpoints of each interval, as they determine whether the function is defined at those specific points.

f(x) = -5, if 2 ≤ x < 3; -4, if 3 ≤ x < 4; -3, if 4 ≤ x < 5; -2, if 5 ≤ x < 6; -1, if 6 ≤ x < 7. Find (a) Domain of f, (b) Range of f, (c) f(2), (d) f(3), (e) f(7), (f) f(3.18), (g) f(sqrt(20.14))

Learn how to find the domain and range of a piecewise function and evaluate it at specific points. The function involves different values for specific intervals of x, and the solution involves calculating f(2), f(3), f(7), f(3.18), and f(sqrt(20.14)).

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