https://file.aiquickdraw.com/mathbot/file/1726141331009vkk3bqhe.jpg

In the image, you have two sets of mathematical functions. The first set, numbered 1 through 5, shows a variety of functions \( f(x) \), \( g(x) \), and \( h(x) \). The second part, labeled **Activity 13.2**, instructs you to "illustrate the graph of the given functions" and provides six different functions.

Here’s the breakdown:

### First Set of Functions:
1. \( f(x) = x + 2 \)
2. \( g(x) = 12x - 1 \)
3. \( h(x) = \frac{-x}{4} \)
4. \( f(x) = x \)
5. \( g(x) = \frac{3x + 5}{8} \)

### Activity 13.2: Illustrate the Graph
1. \( f(x) = 3x - 4 \)
2. \( f(x) = 5x + 3 \)
3. \( f(x) = 7x - 5 \)
4. \( f(x) = \frac{x - 2}{3} \)
5. \( f(x) = \frac{x + 3}{2} \)
6. \( f(x) = \frac{x + 5}{4} \)

These are linear functions of the form \( f(x) = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept.

### Next Steps:
- Do you need help graphing these functions?
- Would you like a detailed explanation of how to solve or graph any of these functions?
  
Feel free to ask for further clarification. Here are some related questions that could expand your understanding:

1. How do you determine the slope and y-intercept of a linear function?
2. What are the steps to graph a function by hand?
3. How do you convert a fraction slope like in \( \frac{x - 2}{3} \) to a graph?
4. How can you compare the steepness of different linear functions?
5. What happens when you graph horizontal or vertical shifts in linear functions?

**Tip**: Always plot the y-intercept first when graphing linear functions, then use the slope to determine the direction and steepness of the line.

Illustrate the graph of the given functions: 1. f(x) = 3x - 4, 2. f(x) = 5x + 3, 3. f(x) = 7x - 5, 4. f(x) = (x - 2) / 3, 5. f(x) = (x + 3) / 2, 6. f(x) = (x + 5) / 4

Learn how to graph various linear functions including f(x) = 3x - 4, f(x) = 5x + 3, and others. This activity covers key concepts like slope, y-intercept, and graphing techniques. Ideal for students in Grades 9-12.

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