https://file.aiquickdraw.com/mathbot/file/1727460038163jpx4qrzz.jpg

Let's break down Problem 17 step by step.

The function \( g \) is represented by the table on the right, where the x-values (domain) are along the bottom (0, 1, 2, 3), and the y-values (range of \( g(x) \)) are along the left side (0, 1, 2, 3).

### Steps:
1. **Domain of \( g \)**: \( A = \{0, 1, 2, 3\} \) (This is provided.)
   
2. **Codomain of \( g \)**: \( B = \{0, 1, 2, 3\} \) (This is also provided.)

3. **Image of \( A \) under \( g \)**: We need to find \( g(x) \) for each \( x \in A \) based on the graph.

   From the graph:
   - \( g(0) = 0 \)
   - \( g(1) = 2 \)
   - \( g(2) = 3 \)
   - \( g(3) = 1 \)

   So, the image of \( A \) under \( g \) is \( \{0, 1, 2, 3\} \).

4. **Find \( g \) evaluated at all elements of its domain**:
   Based on the graph:
   - \( g(0) = 0 \)
   - \( g(1) = 2 \)
   - \( g(2) = 3 \)
   - \( g(3) = 1 \)

5. **The type of function**: 
   The function \( g \) appears to be a **bijection** (both injective and surjective) because every element in the domain has a unique output, and every element in the codomain is mapped.

Would you like me to clarify any part of this solution or provide further details?

Here are 5 related questions to expand your understanding:
1. What is the difference between the codomain and the image of a function?
2. How can you tell if a function is injective by looking at a graph?
3. What conditions are necessary for a function to be surjective?
4. How do you find the inverse of a bijective function?
5. What does it mean for a function to be neither injective nor surjective?

**Tip**: To check if a function is injective, ensure that no two different inputs map to the same output!

Suppose that the graph of the function g is represented by a table. The domain and codomain of g are given as {0,1,2,3}. Determine the image of A under g, find g evaluated at all elements of its domain, and classify the function g.

Learn how to determine the image of a function and evaluate it based on a graph representation. This problem covers essential concepts in functions and graph analysis, focusing on bijection, injectivity, and surjectivity, suitable for Grades 9-12.

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