https://file.aiquickdraw.com/mathbot/file/1726555137271ld9206a5.jpg

The image you have provided contains two graphs labeled (a) and (b). Your task is to copy the graphs and draw the inverse function of each. Let's analyze both graphs to understand how their inverses would look.

### Graph (a):
- This graph shows a linear function with a negative slope passing through the point (0, 0).
- The key points on the graph are:
  - It passes through \( (1, 3) \) and \( (-1, -3) \).

#### Inverse of Graph (a):
- The inverse of a function is obtained by swapping the \( x \) and \( y \) values of each point.
- Key points for the inverse function:
  - The point \( (1, 3) \) becomes \( (3, 1) \).
  - The point \( (-1, -3) \) becomes \( (-3, -1) \).
- The new graph will still be linear but with the inverse slope, passing through these new points.

### Graph (b):
- This graph shows a nonlinear, increasing curve (likely a quadratic) passing through the origin and points \( (2, 2) \) and \( (3, 3) \).
- It looks symmetric about the line \( y = x \).

#### Inverse of Graph (b):
- Since the graph is symmetric, the inverse will look almost identical to the original graph because points like \( (2, 2) \) and \( (3, 3) \) remain unchanged when the \( x \) and \( y \) coordinates are swapped.

Would you like me to generate these inverse graphs visually for you? Also, here are a few follow-up questions that can help reinforce the concept of inverse functions:

1. What is the formal algebraic definition of an inverse function?
2. How can we verify if two functions are inverses of each other?
3. What is the significance of the line \( y = x \) when drawing the inverse of a function?
4. Why do the points on the inverse of graph (b) remain the same after swapping \( x \) and \( y \)?
5. How can you algebraically find the inverse of a given function?

**Tip:** To find the inverse of a function algebraically, swap \( x \) and \( y \) in the equation and solve for \( y \).

Copy the following graphs and draw the graph of each inverse function, based on the provided image.

Learn how to find and draw the inverse functions of given linear and quadratic graphs. Explore key points and symmetry in inverse functions, perfect for Grades 10-12.

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