To solve the questions in the provided image, I’ll address them one by one based on their order in the image:

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Question 1:

"Identify which of the given relations is not a function."

To determine this, check if for each input $x$, there is a unique $y$. If $x$ maps to more than one $y$, it is not a function.

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Question 2:

"Identify the correct graph representing a function $f(x)$."

To verify if a graph represents a function, apply the vertical line test: if any vertical line intersects the graph in more than one point, it is not a function.

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Question 3:

"Determine the domain of the inverse function represented in the given graph."

To find the domain of an inverse function, evaluate the range of the original function since the domain and range swap roles in inverses.

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Question 4:

"Determine the domain of the function $f(x) = \frac{x}{x-2}$."

To find the domain:

• Set the denominator not equal to zero, $x - 2 \neq 0$.
• Thus, $x \neq 2$.
• The domain is all real numbers except $x = 2$.

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Would you like me to explain the reasoning for each step or calculate additional details?

Related Questions for Exploration:

1. What distinguishes a function from a general relation?
2. How do you use the vertical line test to verify functions on a graph?
3. What is the significance of swapping domain and range in inverse functions?
4. How are domains restricted by division or square roots in functions?
5. What are the implications of undefined points in real-life scenarios?

Tip: Always start with identifying the domain before analyzing the graph or