https://file.aiquickdraw.com/mathbot/file/17270601613303umf0kjg.jpg

The given piecewise function is:

\[
g(x) = \begin{cases} 
\frac{5}{x - 2}, & x \neq 2 \\
6, & x = 2 
\end{cases}
\]

We are tasked with evaluating the function at three specific points: \( g(0) \), \( g(-6) \), and \( g(2) \).

### 1. \( g(0) \)
Since \( 0 \neq 2 \), we use the rule \( g(x) = \frac{5}{x - 2} \).
\[
g(0) = \frac{5}{0 - 2} = \frac{5}{-2} = -\frac{5}{2}
\]

### 2. \( g(-6) \)
Since \( -6 \neq 2 \), we again use the rule \( g(x) = \frac{5}{x - 2} \).
\[
g(-6) = \frac{5}{-6 - 2} = \frac{5}{-8} = -\frac{5}{8}
\]

### 3. \( g(2) \)
For \( x = 2 \), the function is defined as \( g(2) = 6 \), as given in the piecewise definition.

### Final answers:
- \( g(0) = -\frac{5}{2} \)
- \( g(-6) = -\frac{5}{8} \)
- \( g(2) = 6 \) (already given as correct in the image)

Do you have any questions or want further details on this?

Here are 5 related questions you might consider:
1. How would the graph of this piecewise function look near \( x = 2 \)?
2. What happens to \( g(x) \) as \( x \) approaches 2 from the left and right?
3. How do you find the limits of the function \( g(x) \) as \( x \) approaches a point where the function is piecewise defined?
4. What is the significance of defining a different value for \( g(2) \) in this piecewise function?
5. How would you evaluate the function for a complex number input, such as \( g(i) \)?

**Tip:** Always check whether the input value matches any specific conditions in a piecewise function before applying the general rule.

Consider the piecewise-defined function:
\[
g(x) = \begin{cases} 
\frac{5}{x - 2}, & x \neq 2 \\
6, & x = 2 
\end{cases}
\]
Evaluate at the given values of the independent variable: g(0), g(-6), g(2).

Explore how to evaluate a piecewise-defined function at different values. This solution covers the steps to compute g(0), g(-6), and g(2) for the given piecewise function, involving algebraic operations and understanding the definition of piecewise functions. Suitable for Grades 9-11.

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