https://file.aiquickdraw.com/mathbot/file/1730517461483kdyafafm.jpg

The function provided in the image is:

\[
f(x) = \frac{3}{2}x - 4
\]

This is a linear function, where:
- The **slope** (or rate of change) is \(\frac{3}{2}\).
- The **y-intercept** is \(-4\), which is the point where the graph of the function intersects the y-axis.

To analyze this function further:
1. **Domain**: The domain of \( f(x) \) is all real numbers, as there are no restrictions on \( x \).
2. **Range**: Since this is a linear function, the range is also all real numbers.
3. **Graph**: The graph of this function would be a straight line with a positive slope, rising from left to right, and intersecting the y-axis at \(-4\).

Would you like further details, or do you have any questions?

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Here are five related questions you might consider:
1. How would you find the x-intercept of \( f(x) = \frac{3}{2}x - 4 \)?
2. What is the effect of changing the slope on the graph of this function?
3. How does the y-intercept affect the position of the graph?
4. How would you find the inverse of \( f(x) = \frac{3}{2}x - 4 \)?
5. How can you determine if this function is increasing or decreasing?

**Tip:** The slope of a linear function determines the steepness and direction of the line; a positive slope means the line goes up as you move right, while a negative slope means it goes down.

Explore the linear function f(x) = (3/2)x - 4 with a breakdown of its slope and y-intercept. This page provides a detailed analysis of the function, suitable for students in Grades 8-10.

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