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The given problem asks to **graph the linear function** and to determine its **domain and range**. The function provided is:

\[
f(x) = -5x + 3
\]

### 1. **Graphing the Linear Function**

The equation \( f(x) = -5x + 3 \) is in the slope-intercept form, \( y = mx + b \), where:
- \( m = -5 \) is the **slope** of the line.
- \( b = 3 \) is the **y-intercept** (where the line crosses the y-axis).

Steps to graph:
1. Start at the **y-intercept** \( (0, 3) \).
2. Use the slope \( -5 \) (which means for every 1 unit you move to the right, you move 5 units down) to plot additional points.
3. Connect the points to form the line.

### 2. **Domain and Range**

- **Domain**: Since this is a linear function, the domain is all real numbers, because you can plug any \( x \)-value into the function.
  
  \[
  \text{Domain} = (-\infty, \infty)
  \]

- **Range**: Similarly, the range is also all real numbers, because the line extends infinitely in both vertical directions as \( x \) increases or decreases.
  
  \[
  \text{Range} = (-\infty, \infty)
  \]

Would you like further details, such as a graph or more explanation on how the slope works? 

Here are 5 related questions to expand on this:
1. What are the key features of a linear function in slope-intercept form?
2. How does changing the slope affect the steepness of the line?
3. How do you find the x-intercept of a linear function?
4. What is the significance of the y-intercept in real-world applications?
5. How can linear functions be used to model real-world scenarios?

**Tip**: When graphing a line, always start with the y-intercept and use the slope to determine the direction and steepness of the line.

Graph the linear function. Give its domain and range. f(x) = -5x + 3

Learn how to graph the linear function f(x) = -5x + 3, determine its domain and range, and understand key concepts such as slope-intercept form. Suitable for students in Grades 8-10.

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