https://file.aiquickdraw.com/mathbot/file/1727209918602v875busl.jpg

The given task asks to reflect the graph of \( y = f(x) \) over the line \( y = x \) to sketch the graph of \( x = f(y) \). Let’s break it down step by step.

### Reflection over \( y = x \):
When you reflect a graph over the line \( y = x \), the coordinates of each point on the graph \( y = f(x) \) are switched. So, a point \( (x, y) \) on \( y = f(x) \) becomes \( (y, x) \) on \( x = f(y) \).

#### a) Reflection of Graph (a):
- The graph in (a) is a line that passes through points like \( (0, 0) \) and \( (1, 2) \).
  - \( (0, 0) \) reflected remains \( (0, 0) \).
  - \( (1, 2) \) becomes \( (2, 1) \).
  - \( (-1, -2) \) becomes \( (-2, -1) \).
- The new graph will still be a straight line, but now it will pass through points like \( (0, 0) \), \( (2, 1) \), and \( (-2, -1) \).

#### b) Reflection of Graph (b):
- The graph in (b) passes through points like \( (-4, 4) \), \( (-2, 0) \), and \( (2, -2) \).
  - \( (-4, 4) \) becomes \( (4, -4) \).
  - \( (-2, 0) \) becomes \( (0, -2) \).
  - \( (2, -2) \) becomes \( (-2, 2) \).
- The reflected graph will have these new points and will look like a curve reflected over the line \( y = x \).

Do you need help sketching this, or more detailed steps on how to plot these points? Let me know if you would like an image to represent the reflection.

### 5 Related Questions:
1. How does reflecting over \( y = x \) affect the slope of a line?
2. What are the properties of a function and its inverse?
3. Can every function be reflected over \( y = x \) to have an inverse?
4. What happens if a graph is not a function but you try to reflect it over \( y = x \)?
5. How do we algebraically determine the inverse of a function?

### Tip:
When reflecting graphs, always switch the x and y coordinates of key points and redraw the graph accordingly to visualize the transformation easily.

Copy each graph and use the reflection line y = x to sketch the graph of x = f(y) on the same set of axes.

Learn how to reflect graphs of functions over the line y = x to find the graph of x = f(y). This problem involves inverse functions and graph transformations, suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation