https://file.aiquickdraw.com/mathbot/file/1728623496313nwopa2zo.jpg

The exercise asks to match the given functions with their inverse graphs. In the images, you are presented with four graphs (labeled a, b, c, and d) representing the inverses and four graphs labeled 13–16 representing the original functions.

To solve these, recall that the graph of a function and its inverse are symmetrical along the line \( y = x \). This reflection symmetry helps identify the pairings. Let's go through each of the graphs systematically:

1. **Graph 13** looks like a linear function with a positive slope. The inverse of this function would also be a linear function, but possibly with a different range of slopes. Comparing it to the given options:
   - (c) matches, as it is also a linear function with a positive slope. So, **13 → (c)**.

2. **Graph 14** is a linear function with a negative slope. The inverse will also be a linear function but reflected. 
   - (b) matches this, since it shows a linear function with a negative slope. Thus, **14 → (b)**.

3. **Graph 15** shows a curve that starts from a low value and rises gradually, resembling a square root function. Its inverse should look like a quadratic function.
   - (a) is a potential match, as it shows a parabolic shape, which could be the inverse of a square root function. Therefore, **15 → (a)**.

4. **Graph 16** is a cubic-like function that passes through the origin and is S-shaped. The inverse should also have a similar shape.
   - (d) is a good match, as it shows an S-shaped curve, the likely inverse of a cubic function. So, **16 → (d)**.

### Final Answers:
- **13 → (c)**
- **14 → (b)**
- **15 → (a)**
- **16 → (d)**

Do you need further details on how inverses work, or do you have any questions?

Here are 5 follow-up questions to explore:
1. How do you reflect a function across the line \(y = x\) to find its inverse graph?
2. What are the conditions for a function to have an inverse that is also a function?
3. How do the slopes of a linear function and its inverse relate to each other?
4. Why do parabolas and square root functions form inverse pairs?
5. What distinguishes a cubic function from other polynomial functions when finding its inverse?

### Tip:
When graphing an inverse function, always check for symmetry along the line \( y = x \) as a quick visual test.

Match the graph of the function with the graph of its inverse function.

Learn how to match functions to their inverse by identifying graph symmetry across the line y = x. Includes exercises on linear, quadratic, cubic, and root functions, ideal for high school students.

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